Methods and apparatus for manipulating droplets by electrowetting-based techniques

ABSTRACT

An apparatus is provided for manipulating droplets. The apparatus is a single-sided electrode design in which all conductive elements are contained on one surface on which droplets are manipulated. An additional surface can be provided parallel with the first surface for the purpose of containing the droplets to be manipulated. Droplets are manipulated by performing electrowetting-based techniques in which electrodes contained on or embedded in the first surface are sequentially energized and de-energized in a controlled manner. The apparatus enables a number of droplet manipulation processes, including merging and mixing two droplets together, splitting a droplet into two or more droplets, sampling a continuous liquid flow by forming from the flow individually controllable droplets, and iterative binary or digital mixing of droplets to obtain a desired mixing ratio.

GOVERNMENT INTEREST

[0001] This invention was made with Government support under Grant No.F30602-98-2-0140 awarded by the Defense Advanced Research ProjectsAgency. The Government has certain rights in the invention.

TECHNICAL FIELD

[0002] The present invention is generally related to the field ofdroplet-based liquid handling and processing, such as droplet-basedsample preparation, mixing, and dilution on a microfluidic scale. Morespecifically, the present invention relates to the manipulation ofdroplets by electrowetting-based techniques.

BACKGROUND ART

[0003] Microfluidic systems are presently being explored for theirpotential to carry out certain processing techniques on capillary-sizedcontinuous flows of liquid. In particular, there is currently greatinterest in developing microfluidic devices commonly referred to as“chemistry-on-a-chip” sensors and analyzers, which are also known aslabs-on-a-chip (LoC) and micro total analysis systems (μ-TAS). Theultimate goal of research in this field is to reduce most common(bio)chemical laboratory procedures and equipment to miniaturized,automated chip-based formats, thereby enabling rapid, portable,inexpensive, and reliable (bio)chemical instrumentation. Applicationsinclude medical diagnostics, environmental monitoring, and basicscientific research.

[0004] On-line monitoring of continuous flows is most often accomplishedby connecting the output of the continuous-flow to the input of a largeanalysis instrument such as a HPLC (high pressure liquidchromatography), CE (capillary electrophoresis) or MS (massspectrometry) system, with appropriate flow control and valving forsample collection and injection. Microfluidic systems for continuousmonitoring typically employ miniaturized analyte-specific biosensorswhere the continuous-flow stream passes over or through a series of thebiosensors. Because the sensors lie in a common channel, crosstalk orcontamination between sensors is often a concern. In analyses where areagent must be mixed with the flow, only one analyte can be measured ata time unless the flow is divided into parallel streams with separatemeans for adding the reagent, controlling and mixing the flow andcarrying out detection in each stream. Additionally, mixing inmicrofluidic flows is usually quite challenging. Sufficient time anddistance must be provided for mixing, which places constraints on chipdesign and system flow rates.

[0005] In general, mixing is a fundamental process in chemical analysisand biological applications. Mixing in microfluidic devices is acritical step in realizing a PTAS (micro total analysis system) or “labon a chip” system. In accordance with the present invention describedhereinbelow, it is posited that mixing in these systems could be usedfor pre-processing sample dilution or for reactions between sample andreagents in particular ratios. It is further posited that the ability tomix liquids rapidly while utilizing minimum chip area would greatlyimprove the throughput of such systems. The improved mixing would relyon two principles: the ability to either create turbulent, nonreversibleflow at such small scales or create multilaminates to enhance mixing viadiffusion.

[0006] Mixers can be broadly categorized into continuous-flow anddroplet-based architectures. A common limitation among allcontinuous-flow systems is that fluid transport is physically confinedto permanently etched structures, and additional mechanisms are requiredto enhance mixing. The transport mechanisms used are usuallypressure-driven by external pumps or electrokinetically-driven byhigh-voltage supplies. This in turn requires the use of valves andcomplex channeling, consuming valuable real estate on a chip. Theserestrictions prevent the continuous-flow micro-mixer from becoming atruly self-contained, reconfigurable lab-on-a-chip. Whereas conventionalcontinuous-flow systems rely on a continuous liquid flow in a confinedchannel, droplet-based systems utilize discrete volumes of liquid. Boththe continuous-flow and droplet-based architectures can be furtherclassified into passive and active mixers. In passive mixers, mixing ismediated through diffusion passively without any external energyinputted for the process. Active mixing, on the other hand, takesadvantage of external energy, through actuation of some sort, to createeither dispersed multilaminates or turbulence. In the microscopic world,effective mixing is a technical problem because it is difficult togenerate turbulent flow by mechanical actuation. The inertial forcesthat produce turbulence and the resulting large interfacial surfaceareas necessary to promote mixing are absent. Thus, mixing that dependson diffusion through limited interfacial areas is a limitation.

[0007] Recently, active mixing by acoustic wave (see Vivek et al.,“Novel acoustic micromixer”, MEMS 2000 p. 668-73); ultrasound (see Yanget al., “Ultrasonic micromixer for microfluidic systems”, MEMS 2000, p.80); and a piezoelectrically driven, valveless micropump (see Yang etal., “Micromixer incorporated with piezoelectrically driven valvelessmicropump”, Micro Total Analysis System '98, p.177-180) have beenproposed, and their effectiveness has been demonstrated. Mixing byelectroosmotic flow has also been described in U.S. Pat. No. 6,086,243to Paul et al. Another mixing technique has been recently presented byemploying chaotic advection for mixing. See Lee et al., “Chaotic mixingin electrically and pressure driven microflows”, The 14th IEEE workshopon MEMS 2001, p.483-485; Liu et al., “Passive Mixing in aThree-Dimensional Serpentine Microchannel”, J. of MEMS, Vol 9 (No. 2),p. 190-197 (June 2000); and Evans et al., “Planar laminar mixer”, Proc.of IEEE, The tenth annual workshop on Micro Electro Mechanical Systems(MEMS 97), p. 96-101 (1997). Lee et al. focus on employingdielectrophoretic forces or pressure to generate chaotic advection,while Liu et al. rely on the geometry of a microchannel to induce thesimilar advection. Evans et al. constructed a planar mixing chamber onthe side of which an asymmetrical source and sink generate a flow field,whereby small differences in a fluid particle's initial location leadsto large differences in its final location. This causes chaoticrearrangement of fluid particles, and thus the mixing two liquids. Mostrecently, a technique has been proposed that uses electrohydrodynamicconvection for active mixing. See Jin et al., “An active micro mixerusing electrohydrodynamic (EHD) convection for microfluidic-basedbiochemical analysis”, Technical Digest, Solid-State Sensor and ActuatorWorkshop, p. 52-55).

[0008] Molecular diffusion plays an important role in small Reynoldsnumber liquid flow. In general, diffusion speed increases with theincrease of the contact surface between two liquids. The time requiredfor molecular diffusion increases in proposition to the square of thediffusion distance. A fast diffusion mixer consisting of a simplenarrowing of a mixing channel has been demonstrated by Veenstra et al.,“Characterization method for a new diffusion mixer applicable in microflow injection analysis systems”, J. Micromech. Microeng., Vol. 9, pg.199-202 (1999). The primary approach for diffusion-based micromixing hasbeen to increase the interfacial area and to decrease the diffusionlength by interleaving two liquids. Interleaving is done by manipulatingthe structure's geometry. One approach is to inject one liquid intoanother through a micro nozzle array. See MiVake et al., “Micro mixerwith fast diffusion”, Proceedings of Micro Electro Mechanical Systems,p. 248-253 (1993). An alternative method is to stack two flow streams inone channel as thin layers by multiple stage splitting and recombining.See Branebierg et al., “Fast mixing by lamination”, Proc. IEEE MicroElectro Mechanical Systems, p. 441 (1996); Krog et al., “Experiments andsimulations on a micro-mixer fabricated using a planar silicon/glasstechnology”, MEMS, p.177-182 (1998); Schwesinger et al., “A modularmicrofluidic system with an integrated micromixer”, J. Micromech.Microeng., Vol 6, pg. 99-102 (1996); and Schwesinger et al., “A staticmicromixer built up in silicon”, Proceedings of the SPIE, TheInternational Society for Optical Engineering, Micromachined Devices andComponents, Vol.2642, p.150-155. The characterizations of this type ofmixer are provided by Koch et al., “Two simple micromixers based onsilicon”, J. Micromech. Microeng., Vol 8, p. 123-126 (1998); Koch etal., “Micromachined chemical reaction system”, Sensors and Actuators,Physical (74), p. 207-210; and Koch et al., “Improved characterizationtechnique for micromixer, J. Micromech. Microeng, Vol 9, p.156-158(1999). A variation of the lamination technique is achieved similarly byfractionation, re-arrangement, and subsequent reunification of liquidsin sinusoidally shaped fluid channels (see Kamper et al., “Microfluidiccomponents for biological and chemical microreactors”, MEMS 1997, p.338); in alternative channels of two counter current liquids (seehttp://www.imm-mainz.de/Lnews/Lnews 4/mire.html); or in a 3D pipe with aseries of stationary rigid elements forming intersecting channels inside(see Bertsch et al., “3D micromixers-downscaling large scale industrialstatic mixers”, MEMS 2001 14^(th) International Conference on MicroElectro Mechanical Systems, p. 507-510). One disadvantage of purelydiffusion-based static mixing is the requirement of a complex 3Dstructure in order to provide out-of-plane fluid flow. Anotherdisadvantage is the low Reynolds number characterizing the flow, whichresults in a long mixing time.

[0009] A problem for active mixers is that energy absorption during themixing process makes them inapplicable to temperature-sensitive fluids.Moreover, some active mixers rely on the charged or polarizable fluidparticles to generate convection and local turbulence. Thus, liquidswith low conductivity could not be properly mixed. When the perturbationforce comes from a mechanical micropump, however, the presence of thevalveless micropump makes the control of flow ratios of solutions formixing quite complex.

[0010] In continuous flow systems, the control of the mixing ratio isalways a technical problem. By varying the sample and reagent flowrates, the mixing ratio can be obtained with proper control of thepressure at the reagent and sample ports. However, the dependence ofpressure on the properties of the fluid and the geometry of the mixingchamber/channels makes the control very complicated. When inlets arecontrolled by a micropump, the nonlinear relationship between theoperating frequency and flow rate make it a nontrivial task to changethe flow rate freely. The discontinuous mixing of two liquids byintegration of a mixer and an electrically actuated flapper valve hasbeen demonstrated by Voldman et al., “An Integrated Liquid MixerNalve”,Journal of Microelectromechanical Systems”, Vol. 9, No. 3 (September2000). The design required a sophisticated pressure-flow calibration toget a range of mixing ratios.

[0011] Droplet-based mixers have been explored by Hosokawa et al.,“Droplet based nano/picoliter mixer using hydrophobic microcapillaryvent”, MEMS '99, p. 388; Hosokawa et al., “Handling of Picoliter LiquidSamples in a Poly(dimethylsiloxane)-Based Microfluidic Device”, Anal.Chem 1999, Vol.71, p.4781-4785; Washizu et al., Electrostatic actuationof liquid droplets for micro-reactor applications, IEEE Transactions onIndustry Applications, Vol. 34 (No. 4), p. 732-737 (1998); Burns et al.,“An Integrated Nanoliter DNA Analysis Device”, Science, Vol. 282 (No.5388), p. 484 (Oct. 16, 1998); Pollack et al., “Electrowetting-basedactuation of liquid droplets for microfluidic applications”, Appl. Phys.Lett., Vol. 77, p. 1725 (September 2000); Pamula et al., “Microfluidicelectrowetting-based droplet mixing”, MEMS Conference, 2001, 8-10;Fowler et al., “Enhancement of Mixing by Droplet-based Microfluidics”,IEEE MEMS Proceedings, 2002, 97-100; Pollack, “Electrowetting-basedmicroactuation of droplets for digital microfluidics”, Ph.D. Thesis,Department of Electrical and Computer Engineering, Duke University; andWu, “Design and Fabrication of an Input Buffer for a Unit FlowMicrofluidic System”, Master thesis, Department of Electrical andComputer Engineering, Duke University.

[0012] It is believed that droplet-based mixers can be designed andconstructed to provide a number of advantages over continuous-flow-basedmicrofluidic devices. Discrete flow can eliminate the limitation on flowrate imposed by continuous microfluidic devices. The design ofdroplet-based mixing devices can be based on a planar structure that canbe fabricated at low cost. Actuation mechanisms based on pneumaticdrive, electrostatic force, or electrowetting do not require heaters,and thus have a minimum effect on (bio) chemistry. By providing a properdroplet generation technique, droplet-based mixers can provide bettercontrol of liquid volume. Finally, droplet-based mixers can enabledroplet operations such as shuttling or shaking to generate internalrecirculation within the droplet, thereby increasing mixing efficiencyin the diffusion-dominated scale.

[0013] In view of the foregoing, it would be advantageous to providenovel droplet-manipulative techniques to address the problems associatedwith previous analytical and mixing techniques that required continuousflows. In particular, the present invention as described and claimedhereinbelow developed in part from the realization that an alternativeand better solution to the continuous flow architecture would be todesign a system where the channels and mixing chambers are notpermanently etched, but rather are virtual and can be configured andreconfigured on the fly. The present invention enables such a system byproviding means for discretizing fluids into droplets and means forindependently controlling individual droplets, allowing each droplet toact as a virtual mixing or reaction chamber.

DISCLOSURE OF THE INVENTION

[0014] The present invention provides droplet-based liquid handling andmanipulation methods by implementing electrowetting-based techniques.The droplets can be sub-microliter-sized, and can be moved freely bycontrolling voltages to electrodes. Generally, the actuation mechanismof the droplet is based upon surface tension gradients induced in thedroplet by the voltage-induced electrowetting effect. The mechanisms ofthe invention allow the droplets to be transported while also acting asvirtual chambers for mixing to be performed anywhere on a chip. The chipcan include an array of electrodes that are reconfigurable in real-timeto perform desired tasks. The invention enables several different typesof handling and manipulation tasks to be performed on independentlycontrollable droplet samples, reagents, diluents, and the like. Suchtasks conventionally have been performed on continuous liquid flows.These tasks include, for example, actuation or movement, monitoring,detection, irradiation, incubation, reaction, dilution, mixing,dialysis, analysis, and the like. Moreover, the methods of the inventioncan be used to form droplets from a continuous-flow liquid source, suchas a from a continuous input provided at a microfluidic chip.Accordingly, the invention provides a method for continuous sampling bydiscretizing or fragmenting a continuous flow into a desired number ofuniformly sized, independently controllable droplet units.

[0015] The partitioning of liquids into discrete, independentlycontrolled packets or droplets for microscopic manipulation providesseveral important advantages over continuous-flow systems. For instance,the reduction of fluid manipulation, or fluidics, to a set of basic,repeatable operations (for example, moving one unit of liquid one unitstep) allows a hierarchical and cell-based design approach that isanalogous to digital electronics.

[0016] In addition to the advantages identified hereinabove, the presentinvention utilizes electrowetting as the mechanism for droplet actuationor manipulation for the following additional advantages:

[0017] 1. Improved control of a droplet's position.

[0018] 2. High parallelism capability with a dense electrode arraylayout.

[0019] 3. Reconfigurability.

[0020] 4. Mixing-ratio control using programming operations, yieldingbetter controllability and higher accuracy in mixing ratios.

[0021] 5. High throughput capability, providing enhanced parallelism.

[0022] 6. Enabling of integration with optical detection that canprovide further enhancement on asynchronous controllability andaccuracy.

[0023] In particular, the present invention provides a sampling methodthat enables droplet-based sample preparation and analysis. The presentinvention fragments or discretizes the continuous liquid flow into aseries of droplets of uniform size on or in a microfluidic chip or othersuitable structure by inducing and controlling electrowetting phenomena.The liquid is subsequently conveyed through or across the structure as atrain of droplets which are eventually recombined for continuous-flow atan output, deposited in a collection reservoir, or diverted from theflow channel for analysis. Alternatively, the continuous-flow stream maycompletely traverse the structure, with droplets removed or sampled fromspecific locations along the continuous flow for analysis. In bothcases, the sampled droplets can then be transported to particular areasof the structure for analysis. Thus, the analysis is carried outon-line, but not in-line with respect to the main flow, allowing theanalysis to be de-coupled from the main flow.

[0024] Once removed from the main flow, a facility exists forindependently controlling the motion of each droplet. For purposes ofchemical analysis, the sample droplets can be combined and mixed withdroplets containing specific chemical reagents formed from reagentreservoirs on or adjacent to the chip or other structure. Multiple-stepreactions or dilutions might be necessary in some cases with portions ofthe chip assigned to certain functions such as mixing, reacting orincubation of droplets. Once the sample is prepared, it can betransported by electrowetting to another portion of the chip dedicatedto detection or measurement of the analyte. Some detection sites can,for example, contain bound enzymes or other biomolecular recognitionagents, and be specific for particular analytes while others can consistof a general means of detection such as an optical system forfluorescence or absorbance based assays. The flow of droplets from thecontinuous flow source to the analysis portion of the chip (the analysisflow) is controlled independently of the continuous flow (the inputflow), allowing a great deal of flexibility in carrying out theanalyses. Other features and advantages of the methods of the presentinvention are described in more detail hereinbelow.

[0025] Methods of the present invention use means for formingmicrodroplets from the continuous flow and for independentlytransporting, merging, mixing, and other processing of the droplets. Thepreferred embodiment uses electrical control of surface tension (i.e.,electrowetting) to accomplish these manipulations. In one embodiment,the liquid is contained within a space between two parallel plates. Oneplate contains etched drive electrodes on its surface while the otherplate contains either etched electrodes or a single, continuous planeelectrode that is grounded or set to a reference potential. Hydrophobicinsulation covers the electrodes and an electric field is generatedbetween electrodes on opposing plates. This electric field creates asurface-tension gradient that causes a droplet overlapping the energizedelectrode to move towards that electrode. Through proper arrangement andcontrol of the electrodes, a droplet can be transported by successivelytransferring it between adjacent electrodes. The patterned electrodescan be arranged in a two dimensional array so as to allow transport of adroplet to any location covered by that array. The space surrounding thedroplets may be filled with a gas such as air or an immiscible fluidsuch as oil.

[0026] In another embodiment, the structure used for ground or referencepotential is co-planar with the drive electrodes and the second plate,if used, merely defines the containment space. The co-planar groundingelements can be a conductive grid superimposed on the electrode array.Alternatively, the grounding elements can be electrodes of the arraydynamically selected to serve as ground or reference electrodes whileother electrodes of the array are selected to serve as drive electrodes.

[0027] Droplets can be combined together by transporting themsimultaneously onto the same electrode. Droplets are subsequently mixedeither passively or actively. Droplets are mixed passively by diffusion.Droplets are mixed actively by moving or “shaking” the combined dropletby taking advantage of the electrowetting phenomenon. In a preferredembodiment, droplets are mixed by rotating them around a two-by-twoarray of electrodes. The actuation of the droplet creates turbulentnon-reversible flow, or creates dispersed multilaminates to enhancemixing via diffusion. Droplets can be split off from a larger droplet orcontinuous body of liquid in the following manner: at least twoelectrodes adjacent to the edge of the liquid body are energized alongwith an electrode directly beneath the liquid, and the liquid moves soas to spread across the extent of the energized electrodes. Theintermediate electrode is then de-energized to create a hydrophobicregion between two effectively hydrophilic regions. The liquid meniscusbreaks above the hydrophobic regions, thus forming a new droplet. Thisprocess can be used to form the droplets from a continuously flowingstream.

[0028] According to one embodiment of the present invention, anapparatus for manipulating droplets comprises a substrate comprising asubstrate surface, an array of electrodes disposed on the substratesurface, an array of reference elements, a dielectric layer disposed onthe substrate surface, and an electrode selector. The reference elementsare settable to a reference potential. The array of reference elementsis disposed of in substantially co-planar relation to the electrodearray, such that each reference element is adjacent to at least one ofthe electrodes. The dielectric layer is disposed on the substratesurface and is patterned to cover the electrodes. The electrode selectorcan be provided as a microprocessor or other suitable component forsequentially activating and de-activating one or more selectedelectrodes of the array to sequentially bias the selected electrodes toan actuation voltage. The sequencing performed by the electrode selectorenables a droplet disposed on the substrate surface to move along adesired path that is defined by the selected electrodes.

[0029] According to one method of the present invention, a droplet isactuated by providing the droplet on a surface that comprises an arrayof electrodes and a substantially co-planar array of reference elements.The droplet is disposed on a first one of the electrodes, and at leastpartially overlaps a second one of the electrodes and an intervening oneof the reference elements disposed between the first and secondelectrodes. The first and second electrodes are activated to spread atleast a portion of the droplet across the second electrode. The firstelectrode is de-activated to move the droplet from the first electrodeto the second electrode.

[0030] According to one aspect of this method, the second electrode isadjacent to the first electrode along a first direction. In addition,the electrode array comprises one more additional electrodes adjacent tothe first electrode along one or more additional directions. The dropletat least partially overlaps these additional electrodes as well as thesecond electrode. In accordance with this aspect of the method, thefirst direction that includes the first electrode and the secondelectrode is selected as a desired direction along which the droplet isto move. The second electrode is selected for activation based on theselection of the first direction.

[0031] In accordance with another method of the present invention, adroplet is split into two or more droplets. A starting droplet isprovided on a surface comprising an array of electrodes and asubstantially co-planar array of reference elements. The electrode arraycomprises at least three electrodes comprising a first outer electrode,a medial electrode adjacent to the first outer electrode, and a secondouter electrode adjacent to the medial electrode. The starting dropletis initially disposed on at least one of these three electrodes, and atleast partially overlaps at least one other of the three electrodes.Each of the three electrodes is activated to spread the starting dropletacross the three electrodes. The medial electrode is de-activated tosplit the starting droplet into first and second split droplets. Thefirst split droplet is disposed on the first outer electrode and thesecond split droplet is disposed on the second outer electrode.

[0032] In yet another method of the present invention, two or moredroplets are merged into one droplet. First and second droplets areprovided on a surface comprising an array of electrodes in asubstantially co-planar array of reference elements. The electrode arraycomprises at least three electrodes comprising a first outer electrode,a medial electrode adjacent to the first outer electrode, and a secondouter electrode adjacent to the medial electrode. The first droplet isdisposed on the first outer electrode and at least partially overlapsthe medial electrode. The second droplet is disposed on the second outerelectrode and at least partially overlaps the medial electrode. One ofthe three electrodes is selected as a destination electrode. Two or moreof the three electrodes are selected for sequential activation andde-activation, based on the selection of the destination electrode. Theelectrodes selected for sequencing are sequentially activated andde-activated to move one of the first and second droplets toward theother droplet, or both of the first and second droplets toward eachother. The first and second droplets merge together to form a combineddroplet on the destination electrode.

[0033] According to one aspect of this method, the first dropletcomprises a first composition, the second droplet comprises a secondcomposition, and the combined droplet comprises both the first andsecond compositions. The method further comprises the step of mixing thefirst and second compositions together. In accordance with the presentinvention, the mixing step can be passive or active. In one aspect ofthe invention, the mixing step comprises moving the combined droplet ona two-by-two sub-array of four electrodes by sequentially activating andde-activating the four electrodes to rotate the combined droplet. Atleast a portion of the combined droplet remains substantially stationaryat or near an intersecting region of the four electrodes while thecombined droplet rotates. In another aspect of the invention, the mixingstep comprises sequentially activating and de-activating a linearlyarranged set of electrodes of the electrode array to oscillate thecombined droplet back and forth along the linearly arranged electrodeset a desired number of times and at a desired frequency. Additionalmixing strategies provided in accordance with the invention aredescribed in detail hereinbelow.

[0034] According to another embodiment of the present invention, anapparatus for manipulating droplets comprises a substrate comprising asubstrate surface, an array of electrodes disposed on the substratesurface, a dielectric layer disposed on the substrate surface andcovering the electrodes, and an electrode selector. The electrodeselector dynamically creates a sequence of electrode pairs. Eachelectrode pair comprises a selected first one of the electrodes biasedto a first voltage, and a selected second one of the electrodes disposedadjacent to the selected first electrode and biased to a second voltagethat is less than the first voltage. Preferably, the second voltage is aground voltage or some other reference voltage. A droplet disposed onthe substrate surface moves along a desired path that runs between theelectrode pairs created by the electrode selector.

[0035] According to yet another method of the present invention, adroplet is actuated by providing the droplet on a surface comprising anarray of electrodes. The droplet is initially disposed on a first one ofthe electrodes and at least partially overlaps a second one of theelectrodes that is separated from the first electrode by a first gap.The first electrode is biased to a first voltage and the secondelectrode is biased to a second voltage lower than the first voltage. Inthis manner, the droplet becomes centered on the first gap. A third oneof the electrodes that is proximate to the first and second electrodesis biased to a third voltage that is higher than the second voltage tospread the droplet onto the third electrode. The bias on the firstelectrode is then removed to move the droplet away from the firstelectrode. The droplet then becomes centered on a second gap between thesecond and third electrodes.

[0036] According to still another method of the present invention, adroplet is split into two or more droplets. A starting droplet isprovided on a surface comprising an array of electrodes. The electrodearray comprises at least three electrodes comprising a first outerelectrode, a medial electrode adjacent to the first outer electrode, anda second outer electrode adjacent to the medial electrode. The startingdroplet is initially disposed on at least one of the three electrodesand at least partially overlaps at least one other of the threeelectrodes. Each of the three electrodes is biased to a first voltage tospread the initial droplet across the three electrodes. The medialelectrode is biased to a second voltage lower than the first voltage tosplit the initial droplet into first and second split droplets. Thefirst split droplet is formed on the first outer electrode and thesecond split droplet is formed on the second outer electrode.

[0037] According to a further method of the present invention, two ormore droplets are merged into one droplet. First and second droplets areprovided on a surface comprising an array of electrodes. The electrodearray comprises at least three electrodes comprising a first outerelectrode, a medial electrode adjacent to the first outer electrode, anda second outer electrode adjacent to the medial electrode. The firstdroplet is disposed on the first outer electrode and at least partiallyoverlaps the medial electrode. The second droplet is disposed on thesecond outer electrode and at least partially overlaps the medialelectrode. One of the three electrodes is selected as a destinationelectrode. Two or more of the three electrodes are selected forsequential biasing based on the selection of the destination electrode.The electrodes selected for sequencing are sequentially biased between afirst voltage and a second voltage to move one of the first and seconddroplets toward the other droplet or both of the first and seconddroplets toward each other. The first and second droplets merge togetherto form a combined droplet on the destination electrode.

[0038] The present invention also provides a method for sampling acontinuous liquid flow. A liquid flow is supplied to a surface along afirst flow path. The surface comprises an array of electrodes and asubstantially co-planar array of reference elements. At least a portionof the liquid flow is disposed on a first one of the electrodes, and atleast partially overlaps a second one of the electrodes and a referenceelement between the first and second electrodes.

[0039] The first electrode, the second electrode, and a third one of theelectrodes adjacent to second electrode are activated to spread theliquid flow portion across the second and third electrodes. The secondelectrode is de-activated to form a droplet from the liquid flow on thethird electrode. The droplet is distinct from and in controllableindependently of the liquid flow.

[0040] In accordance with another method of the present invention forsampling a continuous liquid flow, a liquid flow is supplied to asurface along a first flow path. The surface comprises an array ofelectrodes. At least a portion of the liquid flow is disposed on a firstone of the electrodes and at least partially overlaps a second one ofthe electrodes. The first electrode, the second electrode, and a thirdone of the electrodes adjacent to the second electrode are biased to afirst voltage to spread the liquid flow portion across the second andthird electrodes. The second electrode is biased to a second voltagethat is less than the first voltage to form a droplet from the liquidflow on the third electrode. The droplet so formed is distinct from andcontrollable independently of the liquid flow.

[0041] According to still another embodiment of the present invention, abinary mixing apparatus comprises a first mixing unit, a second mixingunit, and an electrode selector. The first mixing unit comprises a firstsurface area, an array of first electrodes disposed on the first surfacearea, and an array of first reference elements disposed in substantiallyco-planar relation to the first electrodes. The second mixing unitcomprises a second surface area, an array of second electrodes disposedon the second surface area, an array of second reference elementsdisposed in substantially co-planar relation to the second electrodes,and a droplet outlet area communicating with the second surface area andwith the first mixing unit. The electrode selector sequentiallyactivates and de-activates one or more selected first electrodes to mixtogether two droplets supplied to the first surface area. The electrodeselector also sequentially activates and de-activates one or moreselected second electrodes to mix together two other droplets suppliedto the second surface area.

[0042] It is therefore an object of the present invention to sample acontinuous flow liquid input source from which uniformly sized,independently controllable droplets are formed on a continuous andautomated basis.

[0043] It is another object of the present invention to utilizeelectrowetting technology to implement and control droplet-basedmanipulations such as transportation, mixing, detection, analysis, andthe like.

[0044] It is yet another object of the present invention to provide anarchitecture suitable for efficiently performing binary mixing ofdroplets to obtain desired mixing ratios with a high degree of accuracy.

[0045] Some of the objects of the invention having been statedhereinabove, other objects will become evident as the descriptionproceeds when taken in connection with the accompanying drawings as bestdescribed hereinbelow.

BRIEF DESCRIPTION OF THE DRAWINGS

[0046]FIG. 1 is a cross-sectional view of an electrowettingmicroactuator mechanism having a two-sided electrode configuration inaccordance with the present invention;

[0047]FIG. 2 is a top plan view of an array of electrode cells havinginterdigitated perimeters accordance with one embodiment of the presentinvention;

[0048]FIG. 3 is a plot of switching rate as a function of voltagedemonstrating the performance of an electrowetting microactuatormechanism structured in accordance with the present invention;

[0049] FIGS. 4A-4D are sequential schematic views of a droplet beingmoved by the electrowetting technique of the present invention;

[0050] FIGS. 5A-5C are sequential schematic views illustrating twodroplets combining into a merged droplet using the electrowettingtechnique of the present invention;

[0051] FIGS. 6A-6C are sequential schematic views showing a dropletbeing split into two droplets by the electrowetting technique of thepresent invention;

[0052]FIGS. 7A and 7B are sequential schematic views showing a liquidbeing dispensed on an electrode array and a droplet being formed fromthe liquid;

[0053]FIG. 8A is a cross-sectional view illustrating an electrowettingmicroactuator mechanism of the invention implementing a one-dimensionallinear droplet merging process;

[0054]FIG. 8B is a top plan view of the configuration in FIG. 8A withthe upper plane removed;

[0055]FIGS. 9A, 9B, and 9C are respective top plan views of two-,three-, and four-electrode configurations on which one-dimensionallinear mixing of droplets can be performed in accordance with thepresent invention;

[0056]FIGS. 10A, 10B, and 10C are schematic diagrams illustrating theexamples of a mixing-in-transport process enabled by the presentinvention;

[0057]FIG. 11 is a schematic view illustrating a two-dimensional linearmixing process enabled by the present invention;

[0058]FIG. 12A is a top plan view of an array of electrode cells onwhich a two-dimensional loop mixing process is performed in accordancewith the present invention;

[0059]FIG. 12B is a top plan view of a 2×2 array of electrode cells onwhich a two-dimensional loop mixing process is performed in which aportion of the droplet remains pinned during rotation;

[0060]FIG. 13 is a plot of data characterizing the performance of activedroplet mixing using the two-, three- and four-electrode configurationsrespectively illustrated in FIGS. 9A, 9B, and 9C;

[0061]FIG. 14 is a plot of data characterizing the performance of the2×2 electrode configuration illustrated in FIG. 12B;

[0062]FIG. 15A is a schematic view illustrating the formation ofdroplets from a continuous flow source and movement of the dropletsacross an electrode-containing surface to process areas of the surface;

[0063]FIG. 15B is a schematic view illustrating the formation ofdroplets from a continuous flow that traverses an entireelectrode-containing surface or section thereof;

[0064]FIG. 16 is a top plan view of a droplet-to-droplet mixing unitthat can be defined on an electrode array on a real-time basis;

[0065]FIG. 17 is a schematic view of a binary mixing apparatus providedin accordance with the present invention;

[0066]FIG. 18A is a schematic view of the architecture of a binarymixing unit capable of one-phase mixing according to the presentinvention;

[0067]FIG. 18B is a schematic sectional view of the binary mixing unitillustrated in FIG. 18A, showing details of the matrix section thereofwhere binary mixing operations occur;

[0068] FIGS. 19A-19F are sequential schematic views of an electrodearray or section thereof provided by a binary mixing unit of the presentinvention, showing an exemplary process for performing binary mixingoperations to obtain droplets having a predetermined, desired mixingratio;

[0069]FIG. 20 is a schematic view illustrating the architecture for abinary mixing unit capable of two-phase mixing in accordance with thepresent invention;

[0070]FIG. 21 is a plot of mixing points of a one- and two-phase mixingplan enabled by the binary mixing architecture of the present invention;and

[0071]FIG. 22 is a plot of mixing points of a one-, two- and three-phasemixing plan enabled by the binary mixing architecture of the presentinvention;

[0072]FIG. 23A is a cross-sectional view of an electrowettingmicroactuator mechanism having a single-sided electrode configuration inaccordance with another embodiment of the present invention;

[0073]FIG. 23B is a top plan view of a portion of the mechanismillustrated in FIG. 23A with its upper plane removed;

[0074] FIGS. 24A-24D are sequential schematic views of an electrowettingmicroactuator mechanism having an alternative single-sided electrodeconfiguration, illustrating electrowetting-based movement of a dropletpositioned on a misaligned electrode array of the mechanism; and

[0075]FIGS. 25A and 25B are schematic views of an alternativeelectrowetting microactuator mechanism having a single-sided electrodeconfiguration arranged as an aligned array, respectively illustrating adroplet actuated in north-south and east-west directions.

DETAILED DESCRIPTION OF THE INVENTION

[0076] For purposes of the present disclosure, the terms “layer” and“film” are used interchangeably to denote a structure or body that istypically but not necessarily planar or substantially planar, and istypically deposited on, formed on, coats, treats, or is otherwisedisposed on another structure.

[0077] For purposes of the present disclosure, the term “communicate”(e.g., a first component “communicates with” or “is in communicationwith” a second component) is used herein to indicate a structural,functional, mechanical, electrical, optical, or fluidic relationship, orany combination thereof, between two or more components or elements. Assuch, the fact that one component is said to communicate with a secondcomponent is not intended to exclude the possibility that additionalcomponents may be present between, and/or operatively associated orengaged with, the first and second components.

[0078] For purposes of the present disclosure, it will be understoodthat when a given component such as a layer, region or substrate isreferred to herein as being disposed or formed “on”, “in”, or “at”another component, that given component can be directly on the othercomponent or, alternatively, intervening components (for example, one ormore buffer layers, interlayers, electrodes or contacts) can also bepresent. It will be further understood that the terms “disposed on” and“formed on” are used interchangeably to describe how a given componentis positioned or situated in relation to another component. Hence, theterms “disposed on” and “formed on” are not intended to introduce anylimitations relating to particular methods of material transport,deposition, or fabrication.

[0079] For purposes of the present disclosure, it will be understoodthat when a liquid in any form (e.g., a droplet or a continuous body,whether moving or stationary) is described as being “on”, “at”, or“over” an electrode, array, matrix or surface, such liquid could beeither in direct contact with the electrode/array/matrix/surface, orcould be in contact with one or more layers or films that are interposedbetween the liquid and the electrode/array/matrix/surface.

[0080] As used herein, the term “reagent” describes any material usefulfor reacting with, diluting, solvating, suspending, emulsifying,encapsulating, interacting with, or adding to a sample material.

[0081] The droplet-based methods and apparatus provided by the presentinvention will now be described in detail, with reference being made asnecessary to the accompanying FIGS. 1-25B.

Droplet-Based Actuation by Electrowetting

[0082] Referring now to FIG. 1, an electrowetting microactuatormechanism, generally designated 10, is illustrated as a preferredembodiment for effecting electrowetting-based manipulations on a dropletD without the need for pumps, valves, or fixed channels. Droplet D iselectrolytic, polarizable, or otherwise capable of conducting current orbeing electrically charged. Droplet D is sandwiched between a lowerplane, generally designated 12, and an upper plane, generally designated14. The terms “upper” and “lower” are used in the present context onlyto distinguish these two planes 12 and 14, and not as a limitation onthe orientation of planes 12 and 14 with respect to the horizontal.Lower plane 12 comprises an array of independently addressable controlelectrodes. By way of example, a linear series of three control or driveelectrodes E (specifically E₁, E₂, and E₃) are illustrated in FIG. 1. Itwill be understood, however, that control electrodes E₁, E₂, and E₃could be arranged along a non-linear path such as a circle. Moreover, inthe construction of devices benefiting from the present invention (suchas a microfluidic chip), control electrodes E₁, E₂, and E₃ willtypically be part of a larger number of control electrodes thatcollectively form a two-dimensional electrode array or grid. FIG. 1includes dashed lines between adjacent control electrodes E₁, E₂, and E₃to conceptualize unit cells, generally designated C (specifically C₁, C₂and C₃). Preferably, each unit cell C₁, C₂, and C₃ contains a singlecontrol electrode, E₁, E₂, and E₃, respectively. Typically, the size ofeach unit cell C or control electrode E is between approximately 0.05 mmto approximately 2 mm.

[0083] Control electrodes E₁, E₂, and E₃ are embedded in or formed on asuitable lower substrate or plate 21. A thin lower layer 23 ofhydrophobic insulation is applied to lower plate 21 to cover and therebyelectrically isolate control electrodes E₁, E₂, and E₃. Lowerhydrophobic layer 23 can be a single, continuous layer or alternativelycan be patterned to cover only the areas on lower plate 21 where controlelectrodes E₁, E₂ and E₃ reside. Upper plane 14 comprises a singlecontinuous ground electrode G embedded in or formed on a suitable uppersubstrate or plate 25. Alternatively, a plurality of ground electrodes Gcould be provided in parallel with the arrangement of correspondingcontrol electrodes E₁, E₂ and E₃, in which case one ground electrode Gcould be associated with one corresponding control electrode E.Preferably, a thin upper layer 27 of hydrophobic insulation is alsoapplied to upper plate 25 to isolate ground electrode G. Onenon-limiting example of a hydrophobic material suitable for lower layer23 and upper layer 27 is TEFLON® AF 1600 material (available from E. I.duPont deNemours and Company, Wilmington, Del.). The geometry ofmicroactuator mechanism 10 and the volume of droplet D are controlledsuch that the footprint of droplet D overlaps at least two controlelectrodes (e.g., E₁ and E₃) adjacent to the central control electrode(e.g., E₂) while also making contact with upper layer 27. Preferably,this is accomplished by specifying a gap or spacing d, which is definedbetween lower plane 12 and upper plane 14 as being less than thediameter that droplet D would have in an unconstrained state. Typically,the cross-sectional dimension of spacing d is between approximately 0.01mm to approximately 1 mm. Preferably, a medium fills gap d and thussurrounds droplet D. The medium can be either an inert gas such as airor an immiscible fluid such as silicone oil to prevent evaporation ofdroplet D.

[0084] Ground electrode G and control electrodes E₁, E₂ and E₃ areplaced in electrical communication with at least one suitable voltagesource V, which preferably is a DC voltage source but alternativelycould be an AC voltage source, through conventional conductive leadlines L₁, L₂ and L₃. Each control electrode E₁, E₂ and E₃ is energizableindependently of the other control electrodes E₁, E₂ and E₃. This can beaccomplished by providing suitable switches S₁, S₂ and S₃ communicatingwith respective control electrodes E₁, E₂ and E₃, or other suitablemeans for independently rendering each control electrode E₁, E₂ and E₃either active (ON state, high voltage, or binary 1) or inactive (OFFstate, low voltage, or binary 0). In other embodiments, or in otherareas of the electrode array, two or more control electrodes E can becommonly connected so as to be activated together.

[0085] The structure of electrowetting microactuator mechanism 10 canrepresent a portion of a microfluidic chip, on which conventionalmicrofluidic and/or microelectronic components can also be integrated.As examples, the chip could also include resistive heating areas,microchannels, micropumps, pressure sensors, optical waveguides, and/orbiosensing or chemosensing elements interfaced with MOS (metal oxidesemiconductor) circuitry.

[0086] Referring now to FIG. 2, an electrode array or portion thereof isillustrated in which each structural interface between adjacent unitcells (e.g., C₁ and C₂) associated with control electrodes (not shown)is preferably characterized by an interdigitated region, generallydesignated 40, defined by interlocking projections 42 and 43 extendingoutwardly from the main planar structures of respective unit cells C₁and C₂. Such interdigitated regions 40 can be useful in rendering thetransition from one unit cell (e.g., C₁) to an adjacent unit cell (e.g.,C₂) more continuous, as opposed to providing straight-edged boundariesat the cell-cell interfaces. It will be noted, however, that theelectrodes or unit cells according to any embodiment of the inventioncan have any polygonal shape that is suitable for constructing aclosely-packed two-dimensional array, such as a square or octagon.

[0087] Referring back to FIG. 1, the basic electrowetting techniqueenabled by the design of microactuator mechanism 10 will now bedescribed. Initially, all control electrodes (i.e., control electrode E₂on which droplet D is centrally located and adjacent control electrodesE₁ and E₃) are grounded or floated, and the contact angle everywhere ondroplet D is equal to the equilibrium contact angle associated with thatdroplet D. When an electrical potential is applied to control electrodeE₂ situated underneath droplet D, a layer of charge builds up at theinterface between droplet D and energized control electrode E₂,resulting in a local reduction of the interfacial energy YSL. Since thesolid insulator provided by lower hypdrophobic insulating layer 23controls the capacitance between droplet D and control electrode E₂, theeffect does not depend on the specific space-charge effects of theelectrolytic liquid phase of droplet D, as is the case in previouslydeveloped uninsulated electrode implementations.

[0088] The voltage dependence of the interfacial energy reduction isdescribed by $\begin{matrix}{{{\gamma_{SL}(V)} = {{\gamma_{SL}(O)} - {\frac{ɛ}{2d}V^{2}}}},} & (1)\end{matrix}$

[0089] where ε is the permittivity of the insulator, d is the thicknessof the insulator, and V is the applied potential. The change in γ_(SL)acts through Young's equation to reduce the contact angle at theinterface between droplet D and energized control electrode E₂. If aportion of droplet D also overlaps a grounded electrode E₁ or E₃, thedroplet meniscus is deformed asymmetrically and a pressure gradient isestablished between the ends of droplet D, thereby resulting in bulkflow towards the energized electrode E₁ or E₃. For example, droplet Dcan be moved to the left (i.e., to unit cell C₁) by energizing controlelectrode E₁ while maintaining control electrodes E₂ and E₃ at theground state. As another example, droplet D can be moved to the right(i.e., to unit cell C₃) by energizing control electrode E₃ whilemaintaining control electrodes E₁ and E₂ at the ground state.

[0090] The following EXAMPLE describes a prototypical embodiment ofelectrowetting microactuator mechanism 10, with reference beinggenerally made to FIGS. 1 and 2.

EXAMPLE

[0091] A prototype device consisting of a single linear array of seveninterdigitated control electrodes E at a pitch of 1.5 mm was fabricatedand tested. Control electrodes E were formed by patterning a 2000-Åthick layer of chrome on a glass lower plate 21 using standardmicrofabrication techniques. The chips were then coated with a 7000 Ålayer of Parylene C followed by a layer 23 of approximately 2000 Å ofTEFLON® AF 1600. Ground electrode G consisted of an upper plate 25 ofglass coated with a conducting layer (R

s

<20 Ω/square) of transparent indium-tin-oxide (ITO). A thin (˜500 Å)layer 27 of TEFLON® AF 1600 was also applied to ground electrode G. Thethin TEFLON® coating on ground electrode G served to hydrophobize thesurface, but was not presumed to be insulative. After coating withTEFLON®, both surfaces had a contact angle of 104° with water.

[0092] Water droplets (0.7-1.0 μl) of 100 mM KCl were dispensed onto thearray using a pipette, and upper plate 25 was positioned to provide agap d of 0.3 mm between the opposing electrodes E and G. A customizedclamp with spring-loaded contact pins (not shown) was used to makeconnections to the bond pads. A computer was used to control acustom-built electronic interface which was capable of independentlyswitching each output between ground and the voltage output of a 120 VDC power supply.

[0093] A droplet D was initially placed on the center of the groundedcontrol electrode (e.g., E₂) and the potential on the adjacent electrode(e.g., control electrode E₁ or E₃) was increased until motion wasobserved. Typically, a voltage of 30-40 V was required to initiatemovement of droplet D. Once this threshold was exceeded, dropletmovement was both rapid and repeatable. It is believed that contactangle hysteresis is the mechanism responsible for this threshold effect.By sequentially energizing four adjacent control electrodes E at 80 V ofapplied potential, droplet D was moved repeatedly back and forth acrossall four control electrodes E at a switching frequency of 15 Hz.

[0094] The transit time t_(tr) of the droplet D was defined as the timerequired for droplet D to reach the far edge of the adjacent electrodefollowing the application of the voltage potential. The transit timet_(tr) thus represented the minimum amount of time allowed betweensuccessive transfers, and (1/t_(tr)) was the maximum switching rate forcontinuous transfer of a droplet D. The maximum switching rate as afunction of voltage is plotted in FIG. 3, where t_(tr) was determined bycounting recorded video frames of a moving droplet D.

[0095] Sustained droplet transport over 1000's of cycles at switchingrates of up to 1000 Hz has been demonstrated for droplets of 6 nLvolume. This rate corresponds to an average droplet velocity of 10.0cm/s, which is nearly 300 times faster than a previously reported methodfor electrical manipulation of droplets. See M. Washizu, IEEE Trans.Ind. Appl. 34, 732 (1998). Comparable velocities cannot be obtained inthermocapillary systems because (for water) the required temperaturedifference between the ends of droplet D exceeds 100° C. See Sammarco etal., AlChE J., 45, 350 (1999). These results demonstrate the feasibilityof electrowetting as an actuation mechanism for droplet-basedmicrofluidic systems. This design can be extended to arbitrarily largetwo-dimensional arrays to allow precise and independent control overlarge numbers of droplets D and to serve as a general platform formicrofluidic processing.

[0096] Referring now to FIGS. 4A-7B, examples of some basicdroplet-manipulative operations are illustrated. As in the case of FIG.1, a linear arrangement of three unit cells C₁, C₂ and C₃ and associatedcontrol electrodes E₁, E₂ and E₃ are illustrated, again with theunderstanding that these unit cells C₁, C₂ and C₃ and control electrodesE₁, E₂ and E₃ can form a section of a larger linear series, non-linearseries, or two-dimensional array of unit cells/control electrodes. Forconvenience, in FIGS. 4B-7B, corresponding control electrodes and unitcells are collectively referred to as control electrodes E₁, E₂ and E₃.Moreover, unit cells C₁, C₂, and C₃ can be physical entities, such asareas on a chip surface, or conceptual elements. In each of FIGS. 4A-7B,an active (i.e., energized) control electrode E₁, E₂, or E₃ is indicatedby designating its associated electrical lead line L₁, L₂, or L₃ “ON”,while an inactive (i.e., de-energized, floated, or grounded) controlelectrode E₁, E₂, or E₃ is indicated by designating its associatedelectrical lead line L₁, L₂, or L₃ “OFF”.

[0097] Turning to FIGS. 4A-4D, a basic MOVE operation is illustrated.FIG. 4A illustrates a starting position at which droplet D is centeredon control electrode E₁. Initially, all control electrodes E₁, E₂ and E₃are grounded so that droplet D is stationary and in equilibrium oncontrol electrode E₁. Alternatively, control electrode E₁ could beenergized while all adjacent control electrodes (e.g., E₂) are groundedso as to initially maintain droplet D in a “HOLD” or “STORE” state, andthereby isolate droplet D from adjoining regions of an array where othermanipulative operations might be occurring on other droplets. To movedroplet D in the direction indicated by the arrow in FIGS. 4A-4B,control electrode E₂ is energized to attract droplet D and thereby causedroplet D to move and become centered on control electrode E₂, as shownin FIG. 4B. Subsequent activation of control electrode E₃, followed byremoval of the voltage potential at control electrode E₂, causes dropletD to move onto control electrode E₃ as shown in FIG. 4C. This sequencingof electrodes can be repeated to cause droplet D to continue to move inthe desired direction indicated by the arrow. It will also be evidentthat the precise path through which droplet D moves across the electrodearray is easily controlled by appropriately programming an electroniccontrol unit (such as a conventional microprocessor) to activate andde-activate selected electrodes of the array according to apredetermined sequence. Thus, for example, droplet D can be actuated tomake right- and left-hand turns within the array. For instance, afterdroplet D has been moved to control electrode E₂ from E₁ as shown inFIG. 4B, droplet D can then be moved onto control electrode E₅ ofanother row of electrodes E₄-E₆ as shown in FIG. 4D. Moreover, droplet Dcan be cycled back and forth (e.g., shaken) along a desired number ofunit cells and at a desired frequency for various purposes such asagitation of droplet D, as described in the EXAMPLE hereinabove.

[0098] FIGS. 5A-5C illustrate a basic MERGE or MIX operation wherein twodroplets D₁ and D₂ are combined into a single droplet D₃. In FIG. 5A,two droplets D₁ and D₂ are initially positioned at control electrodes E₁and E₃ and separated by at least one intervening control electrode E₂.As shown in FIG. 5B, all three control electrodes E₁, E₂ and E₃ are thenactivated, thereby drawing droplets D₁ and D₂ toward each other acrosscentral control electrode E₂ as indicated by the arrows in FIG. 5B. Oncethe opposing sides of droplets D₁ and D₂ encounter each other at centralcontrol electrode E₂, a single meniscus M is created that joins the twodroplets D₁ and D₂ together. As shown in FIG. 5C, the two outer controlelectrodes E₁ and E₃ are then returned to the ground state, therebyincreasing the hydrophobicity of the surfaces of the unit cellsassociated with outer electrodes E₁ and E₃ and repelling the mergingdroplets D₁ and D₂, whereas energized central control electrode E₂increases the wettability of its proximal surface contacting droplets D₁and D₂. As a result, droplets D₁ and D₂ combine into a single mixeddroplet D₃ as shown in FIG. 5C, which represents the lowest energy statepossible for droplet D₃ under these conditions. The resulting combineddroplet D₃ can be assumed to have twice the volume or mass as either ofthe original, non-mixed droplets D₁ and D₂, since parasitic losses arenegligible or zero. This is because evaporation of the droplet materialis avoided due to the preferable use of a filler fluid (e.g., air or animmiscible liquid such as silicone oil) to surround the droplets,because the surfaces contacting the droplet material (e.g., upper andlower hydrophobic layers 27 and 23 shown in FIG. 1) are low-frictionsurfaces, and/or because the electrowetting mechanism employed by theinvention is non-thermal.

[0099] In the present discussion, the terms MERGE and MIX have been usedinterchangeably to denote the combination of two or more droplets. Thisis because the merging of droplets does not in all cases directly orimmediately result in the complete mixing of the components of theinitially separate droplets. Whether merging results in mixing candepend on many factors. These factors can include the respectivecompositions or chemistries of the droplets to be mixed, physicalproperties of the droplets or their surroundings such as temperature andpressure, derived properties of the droplets such as viscosity andsurface tension, and the amount of time during which the droplets areheld in a combined state prior to being moved or split back apart. As ageneral matter, the mechanism by which droplets are mixed together canbe categorized as either passive or active mixing. In passive mixing,the merged droplet remain on the final electrode throughout the mixingprocess. Passive mixing can be sufficient under conditions where anacceptable degree of diffusion within the combined droplet occurs. Inactive mixing, on the other hand, the merged droplet is then movedaround in some manner, adding energy to the process to effect completeor more complete mixing. Active mixing strategies enabled by the presentinvention are described hereinbelow.

[0100] It will be further noted that in the case where a distinct mixingoperation is to occur after a merging operation, these two operationscan occur at different sections or areas on the electrode array of thechip. For instance, two droplets can be merged at one section, and oneor more of the basic MOVE operations can be implemented to convey themerged droplet to another section. An active mixing strategy can then beexecuted at this other section or while the merged droplet is in transitto the other section, as described hereinbelow.

[0101] FIGS. 6A-6C illustrate a basic SPLIT operation, the mechanics ofwhich are essentially the inverse of those of the MERGE or MIX operationjust described. Initially, as shown in FIG. 6A, all three controlelectrodes E₁, E₂ and E₃ are grounded, so that a single droplet D isprovided on central control electrode E₂ in its equilibrium state. Asshown in FIG. 6B, outer control electrodes E₁ and E₃ are then energizedto draw droplet D laterally outwardly (in the direction of the arrows)onto outer control electrodes E₁ and E₃. This has the effect ofshrinking meniscus M of droplet D, which is characterized as “necking”with outer lobes being formed on both energized control electrodes E₁and E₃. Eventually, the central portion of meniscus M breaks, therebycreating two new droplets D₁ and D₂ split off from the original dropletD as shown in FIG. 6C. Split droplets D₁ and D₂ have the same orsubstantially the same volume, due in part to the symmetry of thephysical components and structure of electrowetting microactuatormechanism 10 (FIG. 1), as well as the equal voltage potentials appliedto outer control electrodes E₁ and E₃. It will be noted that in manyimplementations of the invention, such as analytical and assayingprocedures, a SPLIT operation is executed immediately after a MERGE orMIX operation so as to maintain uniformly-sized droplets on themicrofluidic chip or other array-containing device.

[0102] Referring now to FIGS. 7A and 7B, a DISCRETIZE operation can bederived from the basic SPLIT operation. As shown in FIG. 7A, a surfaceor port I/O is provided either on an electrode grid or at an edgethereof adjacent to electrode-containing unit cells (e.g., controlelectrode E₁), and serves as an input and/or output for liquid. A liquiddispensing device 50 is provided, and can be of any conventional design(e.g., a capillary tube, pipette, fluid pen, syringe, or the like)adapted to dispense and/or aspirate a quantity of liquid LQ. Dispensingdevice 50 can be adapted to dispense metered doses (e.g., aliquots) ofliquid LQ or to provide a continuous flow of liquid LQ, either at portI/O or directly at control electrode E₁. As an alternative to usingdispensing device 50, a continuous flow of liquid LQ could be conductedacross the surface of a microfluidic chip, with control electrodes E₁,E₂, and E₃ being arranged either in the direction of the continuous flowor in a non-collinear (e.g., perpendicular) direction with respect tothe continuous flow. In the specific, exemplary embodiment shown in FIG.7A, dispensing device 50 supplies liquid LQ to control electrode E₁.

[0103] To create a droplet on the electrode array, the control electrodedirectly beneath the main body of liquid LQ (control electrode E₁) andat least two control electrodes adjacent to the edge of the liquid body(e.g., control electrodes E₁ and E₃) are energized. This causes thedispensed body of liquid LQ to spread across control electrodes E₁ andE₂ as shown in FIG. 7A. In a manner analogous to the SPLIT operationdescribed hereinabove with reference to FIGS. 6A-6C, the intermediatecontrol electrode (control electrode E₂) is then de-energized to createa hydrophobic region between two effectively hydrophilic regions. Theliquid meniscus breaks above the hydrophobic region to form or “pinchoff” a new droplet D, which is centered on control electrode E₃ as shownin FIG. 7B. From this point, further energize/de-energize sequencing ofother electrodes of the array can be effected to move droplet D in anydesired row-wise and/or column-wise direction to other areas on theelectrode array. Moreover, for a continuous input flow of liquid LQ,this dispensing process can be repeated to create a train of droplets onthe grid or array, thereby discretizing the continuous flow. Asdescribed in more detail hereinbelow, the discretization process ishighly useful for implementing droplet-based processes on the array,especially when a plurality of concurrent operations on many dropletsare contemplated.

Droplet-Based Mixing Strategies

[0104] Examples of several strategies for mixing droplets in accordancewith the present invention will now be described. Referring to FIGS. 8Aand 8B, a configuration such as that of electrowetting microactuatormechanism 10, described hereinabove with reference to FIG. 1, can beemployed to carry out merging and mixing operations on two or moredroplets, e.g., droplets D₁ and D₂. In FIGS. 8A and 8B, droplets D₁ andD₂ are initially centrally positioned on control electrodes E₂ and E₅,respectively. Droplets D₁ and D₂ can be actuated by electrowetting tomove toward each other and merge together on a final electrode in themanner described previously with reference to FIGS. 5A-5C. The finalelectrode can be an intermediately disposed electrode such as electrodeE₃ or E₄. Alternatively, one droplet can move across one or more controlelectrodes and merge into another stationary droplet. Thus, asillustrated in FIGS. 8A and 8B, droplet D₁ can be actuated to moveacross intermediate electrodes E₃ and E₄ as indicated by the arrow andmerge with droplet D₂ residing on electrode, such that the merging ofdroplets D₁ and D₂ occurs on electrode E₅. The combined droplet can thenbe actively mixed according to either a one-dimensional linear,two-dimensional linear, or two-dimensional loop mixing strategy.

[0105] As one example of a one-dimensional linear mixing strategy,multiple droplets can be merged as just described, and the resultingcombined droplet then oscillated (or “shaken” or “switched”) back andforth at a desired frequency over a few electrodes to causeperturbations in the contents of the combined droplet. This mixingprocess is described in the EXAMPLE set forth hereinabove and caninvolve any number of linearly arranged electrodes, such as electrodesin a row or column of an array. FIGS. 9A, 9B and 9C illustrate two-,three-, and four-electrode series, respectively, in which merging andmixing by shaking can be performed. As another example ofone-dimensional linear mixing, multiple droplets are merged, and thecombined droplet or droplets are then split apart as describedhereinabove. The resulting split/merged droplets are then oscillatedback and forth at a desired frequency over a few electrodes. Thesplit/merged droplets can then be recombined, re-split, andre-oscillated for a number of successive cycles until the desired degreeof mixing has been attained. Both of these one-dimensional, linearmixing approaches produce reversible flow within the combined droplet ordroplets. It is thus possible that the mixing currents established bymotion in one direction could be undone or reversed when the combineddroplet oscillates back the other way. Therefore, in some situations,the reversible flow attending one-dimensional mixing processes mayrequire undesirably large mixing times.

[0106] Referring now to FIGS. 10A-10C, another example ofone-dimensional linear mixing referred to as “mixing-in-transport” isillustrated. This method entails combining two or more droplets and thencontinuously actuating the combined droplet in a forward direction alonga desired flow path until mixing is complete. Referring to FIG. 10A, acombined droplet D is transported from a starting electrode E_(o) alonga programmed path of electrodes on the array until it reaches apreselected destination electrode E_(f). Destination electrode E_(f) canbe a location on the array at which a subsequent process such asanalysis, reaction, incubation, or detection is programmed to occur. Insuch a case, the flow path over which combined droplet D is activelymixed, indicated by the arrow, also serves as the analysis flow pathover which the sample is transported from the input to the processingarea on the array. The number of electrodes comprising the selected pathfrom starting electrode E_(o) to destination electrode E_(f) correspondsto the number of actuations to which combined droplet D is subject.Hence, through the use of a sufficient number of intermediate pathelectrodes, combined droplet D will be fully mixed by the time itreaches destination electrode E_(f). It will be noted that the flow pathdoes not reverse as in the case of the afore-described oscillatorymixing techniques. The flow path can, however include one or moreright-angle turns through the x-y plane of the array as indicated by therespective arrows in FIGS. 10A-10C. In some cases, turning the pathproduces unique flow patterns that enhance the mixing effect. In FIG.10B, the flow path has a ladder or step structure consisting of a numberof right-angle turns. In FIG. 10C, destination electrode E_(f) lies inthe same row as starting electrode E_(o), but combined droplet D isactuated through a flow path that deviates from and subsequently returnsto that row in order to increase the number of electrodes over whichcombined droplet D travels and the number of turns executed.

[0107] Referring now to FIG. 11, an example of a two-dimensional linearmixing strategy is illustrated. One electrode row E_(ROW) and oneelectrode column E_(COL) of the array are utilized. Droplets D₁ and D₂are moved toward each other along electrode row E_(ROW) and merged asdescribed hereinabove, forming a merged droplet D₃ centered on theelectrode disposed at the intersection of electrode row E_(ROW) andelectrode column E_(COL). Selected electrodes of electrode columnE_(COL) are then sequentially energized and de-energized in the mannerdescribed hereinabove to split merged droplet D₃ into split droplets D₄and D₅. Split droplets D₄ and D₅ are then moved along electrode columnE_(COL). This continued movement of split droplets D₄ and D₅ enhancesthe mixing effect on the contents of split droplets D₄ and D₅.

[0108] Referring now to FIGS. 12A and 12B, examples of two-dimensionalloop mixing strategies are illustrated. In FIG. 12A, a combined dropletD is circulated clockwise or counterclockwise in a circular, square orother closed loop path along the electrodes of selected rows and columnsof the array, as indicated by the arrow. This cyclical actuation ofcombined droplet D is effected through appropriate sequencing of theelectrodes comprising the selected path. Combined droplet D is cycled inthis manner for a number of times sufficient to mix its contents. Thecycling of combined droplet D produces nonreversible flow patterns thatenhance the mixing effect and reduce the time required for completemixing. In FIG. 12A, the path circumscribes only one central electrodenot used for actuation, although the path could be made larger so as tocircumscribe more central electrodes.

[0109] In FIG. 12B, a sub-array of at least four adjacent electrodesE₁-E₄ is utilized. Combined droplet D is large enough to overlap allfour electrodes E₁-E₄ of the sub-array simultaneously. The larger sizeof combined droplet D could be the result of merging two smaller-sizeddroplets without splitting, or could be the result of first merging twopairs of droplets and thereafter combining the two merged droplets.Combined droplet D is rotated around the sub-array by sequencingelectrodes E₁-E₄ in the order appropriate for effecting either clockwiseor counterclockwise rotation. As compared with the mixing strategyillustrated in FIG. 12A, however, a portion of the larger-sized combineddroplet D remains “pinned” at or near the intersection of the fourelectrodes E₁-E₄ of the sub-array. Thus, combined droplet D in effectrotates or spins about the intersecting region where the pinned portionis located. This effect gives rise to unique internal flow patterns thatenhance the mixing effect attributed to rotating or spinning combineddroplet D and that promote nonreversible flow. Moreover, the ability tomix combined droplet D using only four electrodes E₁-E₄ enables thecyclical actuation to occur at high frequencies and with less powerrequirements.

[0110] The mixing strategy illustrated in FIG. 12B can also beimplemented using other sizes of arrays. For instance, a 2×4 array hasbeen found to work well in accordance with the invention.

[0111] For all of the above-described mixing strategies, it will benoted the droplets involved can be of equal size or unequal volumes. Ina situation where an n:1 volume ratio of mixing is required, theelectrode areas can be proportionately chosen to yield a one-droplet (n)to one-droplet (1) mixing.

[0112]FIG. 13 depicts graphical data illustrating the performance of theone-dimensional linear mixing strategy. The time for complete mixing isplotted as a function of frequency of droplet oscillation (i.e., theswitch time between one electrode and a neighboring electrode). Curvesare respectively plotted for the 2-electrode (see FIG. 9A), 3-electrode(see FIG. 9B), and 4-electrode (see FIG. 9C) mixing configurations.Mixing times were obtained for 1, 2, 4, 8, and 16 Hz frequencies. Theactuation voltage applied to each electrode was 50 V. It was observedthat increasing the frequency of switching results in faster mixingtimes. Similarly, for a given frequency, increasing the number ofelectrodes also results in improved mixing. It was concluded thatincreasing the number of electrodes on which the oscillation of themerged droplets is performed increases the number of multi-laminateconfigurations generated within the droplet, thereby increasing theinterfacial area available for diffusion.

[0113]FIG. 14 depicts graphical data illustrating the performance of thetwo-dimensional loop mixing strategy in which the droplet is largeenough to overlap the 2×2 electrode sub-array (see FIG. 12B). Mixingtimes were obtained for 8, 16, 32, and 64 Hz frequencies. As in theexperiment that produced the plot of FIG. 13, the actuation voltageapplied to each electrode was 50 V. It was concluded thattwo-dimensional mixing reduces the effect of flow reversibilityassociated with one-dimensional mixing. Moreover, the fact that thedroplet rotates about a point enabled the switching frequency to beincreased up to 64 Hz for an actuation voltage of 50 V. This frequencywould not have been possible in a one-dimensional linear actuation caseat the same voltage. It is further believed that the fact that thedroplet overlaps all four electrodes simultaneously enabled droplettransport at such high frequencies and low voltages. The time betweenthe sequential firing of any two adjacent electrodes of the 2×2sub-array can be reduced because the droplet is in electricalcommunication with both electrodes simultaneously. That is, the lag timeand distance needed for the droplet to physically move from oneelectrode to another is reduced. Consequently, the velocity of thedroplet can be increased in the case of two-dimensional mixing, allowingvortices to form and thereby promoting mixing.

Droplet-Based Sampling and Processing

[0114] Referring now to FIGS. 15A and 15B, a method for sampling andsubsequently processing droplets from a continuous-flow fluid inputsource 61 is schematically illustrated in accordance with the invention.More particularly, the method enables the discretization ofuniformly-sized sample droplets S from continuous-flow source 61 bymeans of electrowetting-based techniques as described hereinabove, inpreparation for subsequent droplet-based, on-chip and/or off-chipprocedures (e.g., mixing, reacting, incubation, analysis, detection,monitoring, and the like). In this context, the term “continuous” istaken to denote a volume of liquid that has not been discretized intosmaller-volume droplets. Non-limiting examples of continuous-flow inputsinclude capillary-scale streams, fingers, slugs, aliquots, and metereddoses of fluids introduced to a substrate surface or other plane from anappropriate source or dispensing device. Sample droplets S willtypically contain an analyte substance of interest (e.g., apharmaceutical molecule to be identified such as by mass spectrometry,or a known molecule whose concentration is to be determined such as byspectroscopy). The several sample droplets S shown in FIGS. 15A and 15Brepresent either separate sample droplets S that have been discretizedfrom continuous-flow source 61, or a single sample droplet S movable todifferent locations on the electrode array over time and along variousanalysis flow paths available in accordance with the sequencing of theelectrodes.

[0115] The method can be characterized as digitizing analytical signalsfrom an analog input to facilitate the processing of such signals. Itwill be understood that the droplet-manipulative operations depicted inFIGS. 15A and 15B can advantageously occur on an electrode array asdescribed hereinabove. Such array can be fabricated on or embedded inthe surface of a microfluidic chip, with or without other features ordevices ordinarily associated with IC, MEMS, and microfluidictechnologies. Through appropriate sequencing and control of theelectrodes of the array such as through communication with anappropriate electronic controller, sampling (including droplet formationand transport) can be done on a continuous and automated basis.

[0116] In FIG. 15A, the liquid input flow of continuous-flow source 61is supplied to the electrode array at a suitable injection point.Utilizing the electrowetting-based techniques described hereinabove,continuous liquid flow 61 is fragmented or discretized into a series ortrain of sample droplets S of uniform size. One or more of these newlyformed sample droplets S can then be manipulated according to a desiredprotocol, which can include one or more of the fundamental MOVE, MERGE,MIX and/or SPLIT operations described hereinabove, as well as anyoperations derived from these fundamental operations. In particular, theinvention enables sample droplets S to be diverted from continuousliquid input flow 61 for on-chip analysis or other on-chip processing.For example, FIG. 15A shows droplets being transported alongprogrammable analysis flow paths across the microfluidic chip to one ormore functional cells or regions situated on the surface of microfluidicchip such as cells 63 and 65.

[0117] Functional cells 63 and 65 can comprise, for example, mixers,reactors, detectors, or storage areas. In the case of mixers andreactors, sample droplets S are combined with additive droplets R₁and/or R₂ that are supplied from one or more separate reservoirs orinjection sites on or adjacent to the microfluidic chip and conveyedacross the microfluidic chip according to the electrowetting technique.In the case of mixers, additive droplets R₁ and/or R₂ can be othersample substances whose compositions are different from sample dropletsS. Alternatively, when dilution of sample droplets S is desired,additive droplets R₁ and/or R₂ can be solvents of differing types. Inthe case of reactors, additive droplets R₁ and/or R₂ can containchemical reagents of differing types. For example, the electrode arrayor a portion thereof could be employed as a miniaturized version ofmulti-sample liquid handling/assaying apparatus, which conventionallyrequires the use of such large components as 96-well microtitre plates,solvent bottles, liquid transfer tubing, syringe or peristaltic pumps,multi-part valves, and robotic systems.

[0118] Functional cells 63 and 65 preferably comprise one or moreelectrode-containing unit cells on the array. Such functional cells 63and 65 can in many cases be defined by the sequencing of theircorresponding control electrodes, where the sequencing is programmed aspart of the desired protocol and controlled by an electronic controlunit communicating with the microfluidic chip. Accordingly, functionalcells 63 and 65 can be created anywhere on the electrode array of themicrofluidic chip and reconfigured on a real-time basis. For example,FIG. 16 illustrates a mixer cell, generally designated MC, that can becreated for mixing or diluting a sample droplet S with an additivedroplet R according to any of the mixing strategies disclosed herein.Mixer cell MC comprises a 5×3 matrix of electrode-containing unit cellsthat could be part of a larger electrode array provided by the chip.Mixer cell MC is thus rendered from five electrode/cell rows ROW1-ROW5and three electrode/cell columns COL1-COL3. MERGE and SPLIT operationscan occur at the centrally located electrodes E₁-E₃ as describedhereinabove with reference to FIGS. 5A-6C. The electrodes associatedwith outer columns COL1 and COL3 and outer rows ROW1 and ROW5 can beused to define transport paths over which sample droplet S and additivedroplet R are conveyed from other areas of the electrode array, such asafter being discretized from continuous-flow source 61 (see FIG. 15A or15B). A 2×2 sub-array can be defined for implementing two-dimensionalloop mixing processes as illustrated in FIG. 12B. During a MIX, MERGE,SPLIT, or HOLD operation, some or all of the electrodes associated withouter columns COL1 and COL3 and outer rows ROW1 and ROW5 can be groundedto serve as gates and thus isolate mixer cell MC from other areas on thechip. If necessary, complete or substantially complete mixing can beaccomplished by a passive mechanism such as diffusion, or by an activemechanism such as by moving or “shaking” the combined droplet accordingto electrowetting as described hereinabove.

[0119] The invention contemplates providing other types of functionalcells, including functional cells that are essentially miniaturizedembodiments or emulations of traditional, macro-scale devices orinstruments such as reactors, detectors, and other analytical ormeasuring instruments. For example, a droplet could be isolated and heldin a single row or column of the main electrode array, or at a cellsituated off the main array, to emulate a sample holding cell or flowcell through which a beam of light is passed in connection with knownoptical spectroscopic techniques. A light beam of an initial intensitycould be provided from an input optical fiber and passed through thedroplet contained by the sample cell. The attenuated light beam leavingthe droplet could then enter an output optical fiber and routed to anappropriate detection apparatus such as a photocell. The optical fiberscould be positioned on either side of the sample cell, or could beprovided in a miniature dip probe that is incorporated with or insertedinto the sample cell.

[0120] Referring back to FIG. 15A, upon completion of a process executedat a functional cell (e.g., cell 63 or 65), the resulting productdroplets (not shown) can be conveyed to respective reservoirs 67 or 69located either on or off the microfluidic chip for the purpose of wastecollection, storage, or output. In addition, sample droplets S and/orproduct droplets can be recombined into a continuous liquid output flow71 at a suitable output site on or adjacent to the microfluidic chip forthe purposes of collection, waste reception, or output to a furtherprocess. Moreover, the droplets processed by functional cell 63 or 65can be prepared sample droplets that have been diluted and/or reacted inone or more steps, and then transported by electrowetting to anotherportion of the chip dedicated to detection or measurement of theanalyte. Some detection sites can, for example, contain bound enzymes orother biomolecular recognition agents, and be specific for particularanalytes. Other detection sites can consist of a general means ofdetection such as an optical system for fluorescence- orabsorbance-based assays, an example of which is given hereinabove.

[0121] In the alternative embodiment shown in FIG. 15B, continuousliquid flow 61 is supplied from an input site 61A, and completelytraverses the surface of the microfluidic chip to an output site 61B. Inthis embodiment, sample droplets S are formed (i.e., continuous liquidinput flow 61 is sampled) at specific, selectable unit-cell locationsalong the length of continuous liquid input flow 61 such as theillustrated location 73, and subsequent electrowetting-basedmanipulations are executed as described hereinabove in relation to theembodiment of FIG. 15A.

[0122] The methods described in connection with FIGS. 15A and 15B haveutility in many applications. Applications of on-line microfluidicanalysis can include, for example, analysis of microdialysis or otherbiological perfusion flows, environmental and water quality monitoringand monitoring of industrial and chemical processes such asfermentation. Analysis can include the determination of the presence,concentration or activity of any specific substance within the flowingliquid. On-line continuous analysis is beneficial in any applicationwhere real-time measurement of a time-varying chemical signal isrequired, a classic example being glucose monitoring of diabeticpatients. Microfluidics reduces the quantity of sample required for ananalysis, thereby allowing less invasive sampling techniques that avoiddepleting the analyte being measured, while also permitting miniaturizedand portable instruments to be realized.

[0123] The droplet-based methods of the invention provide a number ofadvantages over known continuous flow-based microscale methods as wellas more conventional macroscale instrument-based methods. Referring toeither FIG. 15A or 15B, the flow of sample droplets S fromcontinuous-flow source 61 to the analysis portion of the chip (i.e., theanalysis flow) is controlled independently of the continuous flow (i.e.,the input flow), thereby allowing a great deal of flexibility incarrying out the analyses. The de-coupling of the analysis flow from thecontinuous input flow allows each respective flow to be separatelyoptimized and controlled. For example, in microdialysis, the continuousflow can be optimized to achieve a particular recovery rate while theanalysis flow is optimized for a particular sensitivity or samplingrate. Reagent droplets R can be mixed with sample droplets S in theanalysis flow without affecting or contaminating the main input flow.Sample droplets S in the analysis flow can be stored or incubatedindefinitely without interrupting the input flow. Analyses requiringdifferent lengths of time can be carried out simultaneously and inparallel without interrupting the input flow.

[0124] In either embodiment depicted in FIG. 15A or 15B, the analysis orother processing of sample droplets S is carried out on-line insofar asthe analysis occurs as part of the same sequential process as the inputof continuous-flow source 61. However, the analysis is not carried outin-line with respect to continuous liquid input flow 61, because newlyformed sample droplets S are diverted away from continuous liquid inputflow 61. This design thus allows the analysis flow to be de-coupled fromthe input flow.

[0125] As another advantage, multiple analytes can be simultaneouslymeasured. Since continuous liquid flow 61 is fragmented into sampledroplets S, each sample droplet S can be mixed with a different reagentdroplet R₁ or R₂ or conducted to a different test site on the chip toallow simultaneous measurement of multiple analytes in a single samplewithout cross-talk or cross-contamination. Additionally, multiple stepchemical protocols are possible, thereby allowing a wide range of typesof analyses to be performed in a single chip.

[0126] Moreover, calibration and sample measurements can be multiplexed.Calibrant droplets can be generated and measured between samples.Calibration does not require cessation of the input flow, and periodicrecalibration during monitoring is possible. In addition, detection orsensing can be multiplexed for multiple analytes. For example, a singlefluorimeter or absorbance detector may be utilized to measure multipleanalytes by sequencing the delivery of sample droplets S to the detectorsite.

[0127] Another important advantage is the reconfigurability of theoperation of the chip. Sampling rates can be dynamically varied throughsoftware control. Mixing ratios, calibration procedures, and specifictests can all be controlled through software, allowing flexible andreconfigurable operation of the chip. Feedback control is possible,which allows analysis results to influence the operation of the chip.

Droplet-Based Binary Interpolating Digital Mixing

[0128] Referring now to FIG. 17, a binary mixing apparatus, generallydesignated 100, is illustrated in accordance with the invention. Binarymixing apparatus 100 is useful for implementing a droplet-based,variable dilution binary mixing technique in one, two or more mixingphases to obtain desired mixing ratios. The degree of precision of theresulting mixing ratio depends on the number of discrete binary mixingunits utilized. As one example, FIG. 17 schematically illustrates afirst binary mixing unit 110 and a second binary mixing unit 210. Whenmore than one mixing unit is provided, a buffer 310 is preferablyprovided in fluid communication with the mixing units to storeintermediate products and transfer intermediate products between themixing units as needed. A suitable electronic controller EC such as amicroprocessor capable of executing the instructions of a computerprogram communicates with first binary mixing unit 110, second binarymixing unit 210, and buffer 310 through suitable communication lines111, 211, and 311, respectively.

[0129] Binary mixing apparatus 100 can be fabricated on a microfluidicchip for the purpose of carrying out binary interpolating digital mixingprocedures in accordance with the invention. In designing the physicallayouts of the various droplet-handling components of binary mixingapparatus 100 (examples of which are illustrated in FIGS. 18A and 20),electrode design and transportation design (scheduling) were considered.The particular physical layout at least in part determines the code orinstruction set executed by electronic controller EC to control theelectrodes and thus the types and sequences of droplet-basedmanipulation to be performed. Preferably, the electrode-containingdroplet-handling regions of binary mixing apparatus 100 are structuredas shown in the cross-sectional view of FIG. 1, described hereinabove inconnection with electrowetting microactuator mechanism 10, or accordingto a single-sided electrode configurations described hereinbelow. Theelectrodes of each mixing unit can be sequenced to implement any of themixing strategies disclosed herein.

[0130] The architecture of binary mixing apparatus 100 is designed totake full advantage of accelerated rates observed in droplet-to-dropletmixing experiments, while allowing precisely controlled mixing ratiosthat can be varied dynamically for multi-point calibrations. As willbecome evident from the description herein, binary mixing apparatus 100can handle a wide range of mixing ratios with certain accuracy, andenables mixing patterns that demonstrate high parallelism in the mixingoperation as well as scalability in the construction of mixingcomponents in a two-dimensional array. Binary mixing apparatus 100 canhandle a wide range of droplet sizes. There is, however, a lower limiton droplet size if sample droplets are being prepared for the purpose ofa detection or measurement.

[0131] The architecture of binary mixing apparatus 100 is based on therecognition that the most efficient mixing most likely occurs betweentwo droplets moving toward each other. This has been observed fromexperiments, and could be explained by the fact that convection inducedby shear movement of fluids accelerates the mixing process much fasterthan pure physical diffusion. Thus, as a general design principle,one-by-one mixing is utilized as much as possible. As indicatedhereinabove, one-by-one mixing preferably involves both mixing andsplitting operations to maintain uniform droplet size. The basic MIX andSPLIT operations have been described hereinabove with reference to FIGS.5A-6C.

[0132] Certain assumptions have been made in design of the architectureof binary mixing apparatus 100, and include the following:

[0133] 1. Full mixing occurs in terms of chemical and/or physicalprocesses given adequate time.

[0134] 2. Equal droplet splitting occurs in terms of physical volume andchemical components.

[0135] 3. Negligible residues are produced during droplettransportation.

[0136] 4. Mixing time for large dilution ratios is a bottleneck.

[0137] 5. There are tolerances on mixing ratios.

[0138] 6. Transportation time is negligible compared to mixing.

[0139] Preferred design requirements and constraints were alsoconsidered, and include the following:

[0140] 1. Minimum volume of mixture output to guarantee detectability.

[0141] 2. Maximum number of independent control electrodes.

[0142] 3. Maximum mixing area.

[0143] 4. Maximum number of actuation per electrode.

[0144] 5. Reconfigurability for different mixing ratios.

[0145] Thus, one design objective was to complete the mixing processusing a minimum number of mixing-splitting operations while maintainingthe accuracy of the mixing ratio.

[0146] Moreover, some desirable attributes for an ideal mixingarchitecture were considered to be as follows:

[0147] 1. Accurate mixing ratio.

[0148] 2. Small number of mixing cycles. Since many mixing processeswill involve more than one mixing phase, during the first phase the twobinary mixing units 110 and 210 are operated in parallel to andindependent of each other. The second mixing phase, however, can onlystart after the first phase is finished. Thus, the total mixing time oftwo-phase mixing should be the maximum mixing time of first and secondbinary mixing units 110 and 210 in the first phase plus the mixing timeof either first binary mixing unit 110 or second binary mixing unit 210in the second phase. Accordingly, the mixing cycle is defined as thetotal mixing time required to finish one mixing process. It isstandardized in terms of mixing operations, which are assumed to be themost time consuming operations as compared to, for example, droplettransport.

[0149] 3. Small number of total mixing operations. A single binarymixing operation that consists of mixing, splitting and/ortransportation is a source of error. Also, more mixing operations alsomean more usage of the electrodes, which may be another cause of errordue to the charge accumulation on electrodes.

[0150] 4. Simplicity of operations.

[0151] 5. Scalability. The capability of the binary mixing apparatus 100to handle different mixing ratios and extendibility of the structure tomultiple mixing units when large throughput is demanded.

[0152] 6. Parallelism.

[0153] The architecture of binary mixing apparatus 100 implementsmultiple hierarchies of binary mixing phases, with the first hierarchyproviding the approximate mixing ratio and the following ones employedas the calibration mechanism. The concept is analogous to aninterpolating Digital-to-Analog Converter (DAC) whose architecture isdivided into two parts, with the main DAC handling the MSB (mostsignificant bit) in a binary manner and the sub-DAC dealing withcalibration and correction down to the LSB (least significant bit). Anexample of a one-phase binary mixing process carried out to producesixteen sample droplets diluted to a concentration of 1/32 is describedhereinbelow with reference to FIGS. 19A-19F.

[0154] It is believed that mixing in a binary manner results in dilutionto large ratios in the power of two with only a few mixing operations.The accuracy of the ratio can be calibrated by further mixing twointermediate products in a binary manner. For example, one mixingprocess could produce concentrations of 1/8, and another could produceconcentrations of 1/16. When these two mixtures further mix with 1:1,1:3, 3:1, 1:7, and 7:1 ratios, respectively, the final product wouldhave concentrations of 1/10.67, 1/12.8, 1/9.14, 1/14.2, and 1/8.53,respectively. Based on this principle, any ratio can be obtained in afew mixing phases with acceptable tolerance. If further accuracy isneeded, an additional mixing phase using products from the previousphase can be used to calibrate the ratio. As indicated previously, theprocess of approaching the expected ratio to high accuracy could becharacterized as a successive approximation process that is similar toone used in Analog to Digital converter design. It is an approach thattrades off speed with accuracy. However, the number of mixing phasesrequired for adequate accuracy is surprisingly small. Generally, whenthe required ratio is smaller than 32, two mixing phases are oftenenough. Ratios larger than 32 but smaller than 64 would possibly needthree mixing phases. It is also observed that different combinations ofintermediate products mixed with a range of binary ratios would producemore interpolating points to further increase the accuracy, thuseliminating the necessities of using extra mixing phases.

[0155] Based on known mathematical principles, the architecture ofbinary mixing apparatus 100 can be designed to have preferably twosame-structured mixing units (e.g., first binary mixing unit 110 andsecond binary mixing unit 210 shown in FIG. 17), with each binary mixingunit 110 and 210 handling binary mixing and generating certain volumesof mixture. Each binary mixing unit 110 and 210 can produce differentmixing ratios of a power of two according to different operations. Inthe first mixing phase, the sample is mixed with the reagent with aratio of any of the series (1:1, 1:3, 1:7 . . . 1:2^(n-1)) using twobinary mixing units 110 and 210 in parallel. The products are twomixtures with the same volume. The ratio of the two mixtures isdetermined by the required ratio of the final product, and preferably iscontrolled by a computer program. In a second phase, the two mixturesmix with a certain binary ratio in one of the two units. Buffer 310 isused to store some of the intermediate products when second phase mixingis carried out in one of binary mixing units 110 or 210. Since thevolume of the intermediate product is limited (e.g., 16 droplets), thesecond mixing cannot be carried out with an arbitrarily large binaryratio. From the description herein of the structure and operation ofbinary mixing apparatus 100, it can be demonstrated that the possiblebinary ratio in the following mixing phase is constrained to be lessthan or equal to 31, given that 4 columns and 16 droplets are generatedfrom each unit. Even so, sufficient accuracy could be obtained after asecond phase. If further accuracy is demanded, additional mixing can becarried out to generate a mixture closer to the requirement, using theproduct from the second phase and another mixture with power of twoseries ratio (e.g., a calibration mixture).

[0156] From the description above, it can be observed that generatingpowers of two series mixtures can be a fundamental process in obtainingan expected ratio. The exact ratio of this mixture could be decidedahead of time or varied dynamically. For example, during the first phaseof mixing, the two ratios could be calculated ahead of time according tothe required ratio. In the phase following the second phase, however,the calibration mixture could be decided dynamically, given the feedbackfrom the quality of previous mixing. Even if predecided, it is likelythat extra time would be needed to prepare the calibration mixturebefore a further phase mixing is carried out. In such a case, the use ofonly two binary mixing units 110 and 210 might be not enough, and anextra binary mixing unit could be added to prepare the calibrationmixture in parallel with the previous calibration mixing process.

[0157] The determination of a mixing strategy includes calculating thenumber of mixing phases and the mixing ratio for each phase according tothe required ratio and its tolerance. This determination can be solvedby an optimization process with the number of mixing operations and timeof the mixing as the objective function.

[0158] Referring now to FIGS. 18A and 18B, an exemplary architecture forfirst binary mixing unit 110 is illustrated, with the understanding thatsecond binary mixing unit 210 and any other additional mixing unitsprovided can be similarly designed. The embodiment shown in FIG. 18A iscapable of one-phase mixing, while the embodiment shown in FIG. 20 (tobe briefly described hereinbelow) is capable of two-phase mixing. Asshown in FIG. 18A, first binary mixing unit 110 generally comprises a7×7 electrode matrix or array, generally designated EA, consisting of 49matrix electrodes and their associated cells E_(ij), where “i”designates 1, 2, . . . , 7 rows of electrodes and “j” designates 1, 2, .. . , 7 columns of electrodes. FIG. 18B identifies matrix electrodesE_(ij) of electrode array EA in accordance with a two-dimensional systemof rows ROW1-ROW7 and columns COL1-COL7. The invention, however, is notlimited to any specific number of electrodes, rows, and columns. Alarger or smaller electrode array EA could be provided as appropriate.

[0159] Referring back to FIG. 18A, a sample reservoir 113, wastereservoir 115, and reagent reservoir 117 are also provided. Depending onthe position of reservoirs 113, 115 and 117 in relation to electrodearray EA, a suitable number and arrangement of transport or pathelectrodes and associated cells T₁-T₄ are provided for conveyingdroplets to and from electrode array EA. A number of electrical leads(e.g., L) are connected to matrix electrodes E_(ij) and transportelectrodes T₁-T₄ to control the movement or other manipulation ofdroplets. It will be understood that electrical leads L communicate witha suitable electronic controller such as a microprocessor (e.g.,electronic controller EC in FIG. 17). Each matrix electrode E_(ij) couldhave its own independent electrical lead connection. However, to reducethe number of electrical leads L and hence simplify the architecture offirst binary mixing unit 110, the electrodes of each of columnsCOL2-COL7 (see FIG. 18B) are connected to common electrical leads L asshown in FIG. 18A. These common connections must be taken intoconsideration when writing the protocol for mixing operations to becarried out by first binary mixing unit 110.

[0160] In effect, each binary mixing unit 110 and 210 of binary mixingapparatus 100 is designed to have 4×4 logic cells with each cell storingthe sample, reagent or intermediate mixture. This can be conceptualizedby comparing the matrix layout of FIG. 18B with the 4×4 logic cellmatrix illustrated in FIGS. 19A-19F. The 4×4 construct accounts for thefact that droplets combine on intermediate control electrodes fromadjacent control electrodes (e.g., intermediate control electrode E₂ andadjacent control electrodes E₁ and E₃ in FIGS. 5A-6C), the mixed dropletis then split, and the newly formed mixed droplets are then returned tothe adjacent control electrodes at the completion of the MIX (orMIX-SPLIT) operation. Hence, certain rows of electrodes need only beused as temporary intermediate electrodes during the actual dropletcombination event. The construct also accounts for the fact that certaincolumns of electrodes need only be used for droplet transport (e.g.,shifting droplets from one column to another to make room for theaddition of new reagent droplets). In view of the foregoing, electroderows ROW2, ROW4 and ROW6, and columns COL2, COL4 and COL6 in FIG. 18Bare depicted simply as lines in FIGS. 19A-19F. Also in FIGS. 19A-19F,active electrodes are indicated by shaded bars, mixing operations areindicated by the symbol “----><----”, and transport operations areindicated by the symbol “---->”. Additionally, droplet concentrationsare indicated by numbers (e.g., 0, 1, ½) next to rows and columns wheredroplets reside.

[0161] It can be seen that one-by-one mixing can occur between some ofthe adjacent cells in horizontal or vertical directions (from theperspective of the drawing sheets containing FIGS. 19A-19F), dependingon whether active electrodes exist between the two cells. In the firstcolumn, between any of the two adjacent row cells containing droplets,an active electrode exists that allows the two adjacent row cells toperform mixing operations. In other columns, there are no activeelectrodes between two row cells. This is illustrated, for example, inFIG. 19A. Between any of the columns containing droplets, electrodesexist that allow any of the cells in one column to conduct a mixingoperation with the cells of its adjacent column simultaneously. This isillustrated, for example, in FIG. 19D. By the use of the activeelectrodes, the content of a logic cell (i.e., a droplet) can move fromone row to another in the first column, or move between columns. Theemployment of the 4×4 logic structure is designed for the optimizationof binary operations, as demonstrated by the following example. It willbe noted that the volume output of the present one-mixing-unitembodiment of first binary mixing unit 110 is limited to 16 droplets,although the physical volume of the final product can be adjusted bychanging the size of each droplet.

[0162] To demonstrate how binary mixing apparatus 100 can produce any ofthe power of two ratios, FIGS. 19A-19F illustrate an example of a seriesof mixing operations targeting a 1:31 ratio (equal to 1/32concentration). It can be seen that the mixing process has two basicstages: a row mix and a column mix. Generally, the purpose of the rowmix is to approach the range of the mixing ratio with a minimum volumeof two mixing inputs. The purpose of the column mix is to produce therequired volume at the output and at the same time obtain anotherfour-fold increase in ratio. Thus, as indicated in FIGS. 19A-19F, toobtain a 1:31 ratio, the row mix results in a 1:7 ratio or 1/8concentration (see FIG. 19D). The column mix assists in achieving thefinal product ratio of 1:31 or 1/32 concentration (see FIG. 19F).

[0163] Referring specifically to FIG. 19A, a single row mix is performedby combining a sample droplet S₁ having a concentration of 1 (i.e.,100%) with a reagent (or solvent) droplet R₁ having a concentration of0. This results in two intermediate-mixture droplets I₁ and I₂, eachhaving a 1/2 concentration as shown in FIG. 19B. One of theintermediate-mixture droplets (e.g., I₁) is discarded, and a new reagentdroplet R₂ is moved to the logic cell adjacent to the remainingintermediate-mixture droplet (e.g., I₂). Another row mix is performed bycombining intermediate-mixture droplet I₂ and reagent droplet R₂. Thisresults two intermediate-mixture droplets I₃ and I₄, each having a 1/4concentration as shown in FIG. 19C. Two new reagent droplets R₃ and R₄are then added and, in a double row mix operation, combined withrespective intermediate-mixture droplets I₃ and I₄. This results in fourintermediate-mixture droplets I₅-I₈, each having a 1/8 concentration asshown in FIG. 19D.

[0164] As also shown in FIG. 19D, four new reagent droplets R₅-R₈ arethen moved onto the matrix adjacent to respective intermediate-mixturedroplets I₅-I₈. A column mix is then performed as between eachcorresponding pair of intermediate-mixture droplets I₅-I₈ and reagentdroplets R₅-R₈. This produces eight intermediate-mixture dropletsI₉-I₁₆, each having a 1/16 concentration as shown in FIG. 19E. As alsoshown in FIG. 19E, each column of four intermediate-mixture droplets,I₉-I₁₂ and I₁₃-I₁₆, respectively, is shifted over one column to theright to enable two columns of new reagent droplets, R₉-R₁₂ and R₁₃-R₁₆,respectively, to be loaded onto the outer columns of the matrix. Eachcorresponding pair of intermediate-mixture droplets and reagent droplets(e.g., I₉ and R₉, I₁₀ and R₁₀, etc.) is then combined through additionalcolumn mix operations.

[0165] As a result of these mixing operations, sixteen final-mixtureproduct droplets P₁-P₁₆ are produced, each having a final concentrationof 1/32 (corresponding to the target mix ratio of 1:31) as shown in FIG.19F. Product droplets P₁-P₁₆ are now prepared for any subsequentoperation contemplated, such sampling, detection, analysis, and the likeas described by way of example hereinabove. Additionally, depending onthe precise mix ratio desired, product droplets P₁-P₁₆ can be subjectedto a second or even a third phase of mixing operations if needed asdescribed hereinabove. Such additional mixing phases can occur at adifferent area on the electrode array of which first binary mixing unit110 could be a part. Alternatively, as illustrated in FIG. 17, thefinal-mixture droplets can be conveyed to another binary mixingapparatus (e.g., second binary mixing unit 210) that fluidlycommunicates directly with first binary mixing unit 110 or throughbuffer 310.

[0166] The method of the invention can be applied to ratios less than orgreater than 31. For example, if the goal is to obtain a ratio of 1:15,the row mix would mix the input to a ratio of 1:3, which would requiretwo mixing operations instead of three for obtaining a mixing ratio of1:7. In terms of mixing operations, FIGS. 19A-19F can be used to showthat the first stage for row mix (single) and the discard operation forthe second stage could be eliminated in such a case.

[0167] To further explain the detailed operations for completing themixing of 1:31, a pseudo code for the example specifically illustratedin FIGS. 19A-19F (and with general reference to FIG. 18B) is listed asfollows:

[0168] 1. Load S (1,1), Load R (2,1), Row Mix 1,2

[0169] 2. (Discard (1,1), Load R (3,1)), Row Mix 2,3

[0170] 3. Load R (1,1) Load R (3,1), (Row Mix 1,2, Row Mix 3,4)

[0171] 4. Column Load R2, Column Mix 1,2

[0172] 5. Column Move 2 to 3, Column Move 1 to 2, column Load R1, ColumnLoad R4, (Column Mix 1,2 Column Mix 3,4)

[0173] 6. Finish

[0174] The above pseudo code also standardizes the possible mixingoperations into one mixing process. The sequence of the operations issubject to more potential optimization to increase the throughput of themixing while decreasing the number of mixing operations. This designalso keeps in mind that the number of active electrodes should bemaintained as small as possible while making sure all the mixingoperations function properly. In the preferred embodiment, each binarymixing unit 110 and 210 (see FIG. 17) is designed to have 13 activeelectrodes to handle the mixing functions. The capability oftransporting the droplets into and inside the each binary mixing unit110 and 210 is another consideration. Initially, the two outside columnsof the array could be used as transportation channels running along bothsides of the mixer to deliver droplets into the mixer simultaneouslywith other operations of the mixer. The same number of electrodes canalso handle these transportation functions.

[0175] The second phase is the mixing process when the intermediateproducts from two binary mixing units 110 and 210 (see FIG. 17) are tobe mixed. It is similar to the standard binary mixing process in thefirst phase described hereinabove with reference to FIGS. 19A-19F. Theonly difference is that the second-phase mixing is carried out in one ofbinary mixing units 110 and 210 holding the previous mixing product(e.g., product droplets P₁-P₁₆ shown in FIG. 19F). As indicatedpreviously, buffer 310 is used to hold some of the product during theprocess.

[0176] It can be calculated that the maximum ratio of mixing during thesecond phase is limited to 31. The reason is that to obtain the maximumratio, row mixing should be used as much as possible. When row mixing isused to increase the ratio, less input is lost during the discardprocess. Thus, when there are finite amounts of input material, thefirst choice is to see how far the row mixing can go until there is justenough volume left to fulfill the requirement for mixture output. Inthis way, it could be known that two mixtures with 16 droplets can onlymix with the largest ratio of 1:31 when the output requirement isspecified to no less than 16 droplets. It can also be demonstrated fromFIGS. 19A-19F that to mix with a ratio of 1:31, 16 droplets of reagentswould be the minimum amount.

[0177] The physical layout for first binary mixing unit 110 illustratedin FIG. 18A can be modified to better achieve two-phase mixingcapability. Accordingly, referring now to FIG. 20, a two-phase mixingunit, generally designated 410, is illustrated. The architecture oftwo-phase mixing unit 410 is similar to that of first binary mixing unit110 of FIG. 18A, and thus includes the 7×7 matrix, a sample reservoir413, a waste reservoir 415, a reagent reservoir 417, and an appropriatenumber and arrangement of off-array electrodes as needed for transportof droplets from the various reservoirs to the 7×7 matrix. Two-phasemixing unit 410 additionally includes a cleaning reservoir 419 to supplycleaning fluid between mixing processes, as well as an outlet site 421for transporting product droplets to other mixing units or to buffer 310(see FIG. 17). Moreover, it can be seen that additional rows and columnsof electrodes are provided at the perimeter of the 7×7 matrix to providetransport paths for droplets to and from the matrix.

[0178] Further insight into the performance of the architecture ofbinary mixing apparatus 100 can be obtained by considering the TABLE setforth hereinbelow. This TABLE was constructed to list all the possibleinterpolating mixing ratios using a two-phase mixing strategy for amaximum mixing ratio of 63 (or, equivalently, a maximum concentration of1/64). The corresponding mixing parameters, such as the mixing ratio formixing unit 1 and 2 (e.g., first and second binary mixing units 110 and210) in the first phase, the mixing ratio for the second phase, and thetotal mixing cycles are also recorded. The TABLE can serve as a basisfor selecting the proper mixing strategy and/or further optimization interms of trading off accuracy with time, improving resource usage whenmultiple mixers exist, decreasing total mixing operations, improvingparallelism, and so on. The TABLE can be provided as a look-up table ordata structure as part of the software used to control apparatus 100.

[0179] The TABLE shows that there are a total of 196 mixing strategiesusing the architecture of the invention, which corresponds to 152 uniquemixing points. The 196 mixing strategies are calculated by interpolatingany possible combinations of two mixtures with power of two ratios under63. These points have non-linear instead of linear intervals. Thesmaller the ratio, the smaller the interval. The achievable points areplotted in FIG. 21. It is evident from the TABLE that the number ofachievable ratios is larger than traditional linear mixing points andthe distribution is more reasonable. In addition, certain volumes ofoutput other than one droplet can allow more tolerance on the errorcaused by one-by-one mixing. In terms of mixing cycles, the bestperformance is for mixing ratios of the power of two compared to theirnearby ratios. In terms of accuracy, the larger the ratio, generally theworse the performance, since a smaller number of interpolating pointscan be achieved.

[0180] It can be observed from the two-phase mixing plan plotted in FIG.21 that there are not enough points when the target ratio is larger than36. FIG. 21 shows that there is no point around a ratio of 40. Thedifference between the target and theoretical achievable ratio couldamount to 3. However, by careful examination of the achievable pointsaround 40, an appropriate usage of the remaining mixture from phase oneto further calibrate the available points can result in severaladditional interpolating points between 36.5714 and 42.6667, where thelargest error exists from the phase two mixing plan. For instance, themixing plan #183 in the TABLE calls for obtaining mixture 1 and mixture2 with ratios of 1:31 and 1:63, respectively, then mixing them with aratio of 3:1. It is known that there are 3/4 parts of mixture 2 left. Soit is possible to mix the mixture from phase two with a concentration of36.517 with mixture 2 of concentration 63 using ratio of 3:1, 7:1, etc.That leads to a point at 40.9, 38.5, etc. In such manner, more accuracyis possible with an additional mixing phase, but with only a smallincrease in mixing cycles (two and three cycles, respectively, in thisexample), and at the expense of no additional preparation of calibrationmixture.

[0181]FIG. 22 demonstrates all the achievable points by one-phase,two-phase, and three-phase mixing plans. The total number of points is2044. The points achieved by phase three are obtained by using theproduct from phase two and remaining products from phase one. They arecalculated by considering the volume of the remaining product from phaseone after phase two has finished and reusing them to mix with productsfrom phase two. The possible mixing ratios of phase three are determinedby the mixing ratio of phase two. TABLE Total Mix Plan Target Mix Unit 1Mix Unit 2 Phase 2 Mix Number Mix Ratio Mix Ratio Mix Ratio Mix RatioCycles 1 1.0159 1:0 1:1  31:1  6 2 1.0240 1:0 1:3  31:1  7 3 1.0281 1:01:7  31:1  8 4 1.0302 1:0 1:15 31:1  9 5 1.0312 1:0 1:31 31:1  10 61.0317 1:0 1:63 31:1  11 7 1.0323 1:0 1:1  15:1  5 8 1.0492 1:0 1:3 15:1  6 9 1.0579 1:0 1:7  15:1  7 10 1.0622 1:0 1:15 15:1  8 11 1.06441:0 1:31 15:1  9 12 1.0656 1:0 1:63 15:1  10 13 1.0667 1:0 1:1  7:1 4 141.1034 1:0 1:3  7:1 5 15 1.1228 1:0 1:7  7:1 6 16 1.1327 1:0 1:15 7:1 717 1.1378 1:0 1:31 7:1 8 18 1.1403 1:0 1:63 7:1 9 19 1.1429 1:0 1:1  3:13 20 1.2308 1:0 1:3  3:1 4 21 1.2800 1:0 1:7  3:1 5 22 1.3061 1:0 1:153:1 6 23 1.3196 1:0 1:31 3:1 7 24 1.3264 1:0 1:63 3:1 8 25 1.3333 1:01:1  1:1 2 26 1.6000 1:0 1:1  1:3 3 27 1.6000 1:0 1:3  1:1 3 28 1.77781:0 1:1  1:7 4 29 1.7778 1:0 1:7  1:1 4 30 1.8824 1:0 1:1   1:15 5 311.8824 1:0 1:15 1:1 5 32 1.9394 1:0 1:1   1:31 6 33 1.9394 1:0 1:31 1:16 34 1.9692 1:0 1:63 1:1 7 35 2.0000 1:1 N/A N/A 1 36 2.0317 1:1 1:3 31:1  7 37 2.0480 1:1 1:7  31:1  8 38 2.0562 1:1 1:15 31:1  9 39 2.06041:1 1:31 31:1  10 40 2.0624 1:1 1:63 31:1  11 41 2.0645 1:1 1:3  15:1  642 2.0981 1:1 1:7  15:1  7 43 2.1157 1:1 1:15 15:1  8 44 2.1245 1:1 1:3115:1  9 45 2.1289 1:1 1:63 15:1  10 46 2.1333 1:1 1:3  7:1 5 47 2.20691:1 1:7  7:1 6 48 2.2456 1:1 1:15 7:1 7 49 2.2655 1:1 1:31 7:1 8 502.2756 1:1 1:63 7:1 9 51 2.2857 1:0 1:3  1:3 4 52 2.2857 1:1 1:3  3:1 453 2.4615 1:1 1:7  3:1 5 54 2.5600 1:1 1:15 3:1 6 55 2.6122 1:1 1:31 3:17 56 2.6392 1:1 1:63 3:1 8 57 2.6667 1:1 1:3  1:1 3 58 2.9091 1:0 1:3 1:7 5 59 2.9091 1:0 1:7  1:3 5 60 3.2000 1:1 1:3  1:3 4 61 3.2000 1:11:7  1:1 4 62 3.3684 1:0 1:3   1:15 6 63 3.3684 1:0 1:15 1:3 6 64 3.55561:1 1:3  1:7 5 65 3.5556 1:1 1:15 1:1 5 66 3.6571 1:0 1:3   1:31 7 673.6571 1:0 1:31 1:3 7 68 3.7647 1:1 1:3   1:15 6 69 3.7647 1:1 1:31 1:16 70 3.8209 1:0 1:63 1:3 8 71 3.8788 1:1 1:3   1:31 7 72 3.8788 1:1 1:631:1 7 73 4.0000 1:3 N/A N/A 3 74 4.0635 1:3 1:7  31:1  8 75 4.0960 1:31:15 31:1  9 76 4.1124 1:3 1:31 31:1  10 77 4.1207 1:3 1:63 31:1  11 784.1290 1:3 1:7  15:1  7 79 4.1967 1:3 1:15 15:1  8 80 4.2314 1:3 1:3115:1  9 81 4.2490 1:3 1:63 15:1  10 82 4.2667 1:0 1:7  1:7 6 83 4.26671:3 1:7  7:1 6 84 4.4138 1:3 1:15 7:1 7 85 4.4912 1:3 1:31 7:1 8 864.5310 1:3 1:63 7:1 9 87 4.5714 1:1 1:7  1:3 5 88 4.5714 1:3 1:7  3:1 589 4.9231 1:3 1:15 3:1 6 90 5.1200 1:3 1:31 3:1 7 91 5.2245 1:3 1:63 3:18 92 5.3333 1:3 1:7  1:1 4 93 5.5652 1:0 1:7   1:15 7 94 5.5652 1:0 1:151:7 7 95 5.8182 1:1 1:7  1:7 6 96 5.8182 1:1 1:15 1:3 6 97 6.4000 1:31:7  1:3 5 98 6.4000 1:3 1:15 1:1 5 99 6.5641 1:0 1:7   1:31 8 1006.5641 1:0 1:31 1:7 8 101 6.7368 1:1 1:7   1:15 7 102 6.7368 1:1 1:311:3 7 103 7.1111 1:3 1:7  1:7 6 104 7.1111 1:3 1:31 1:1 6 105 7.2113 1:01:63 1:7 9 106 7.3143 1:1 1:7   1:31 8 107 7.3143 1:1 1:63 1:3 8 1087.5294 1:3 1:7   1:15 7 109 7.5294 1:3 1:63 1:1 7 110 7.7576 1:3 1:7  1:31 8 111 8.0000 1:7 N/A N/A 4 112 8.1270 1:7 1:15 31:1  9 113 8.19201:7 1:31 31:1  10 114 8.2249 1:7 1:63 31:1  11 115 8.2581 1:0 1:15  1:158 116 8.2581 1:7 1:15 15:1  8 117 8.3934 1:7 1:31 15:1  9 118 8.4628 1:71:63 15:1  10 119 8.5333 1:1 1:15 1:7 7 120 8.5333 1:7 1:15 7:1 7 1218.8276 1:7 1:31 7:1 8 122 8.9825 1:7 1:63 7:1 9 123 9.1429 1:3 1:15 1:36 124 9.1429 1:7 1:15 3:1 6 125 9.8462 1:7 1:31 3:1 7 126 10.2400  1:71:63 3:1 8 127 10.6667  1:7 1:15 1:1 5 125 10.8936  1:0 1:15  1:31 9 12910.8936  1:0 1:31  1:15 9 130 11.1304  1:1 1:15  1:15 8 131 11.1304  1:11:31 1:7 8 132 11.6364  1:3 1:15 1:7 7 133 11.6364  1:3 1:31 1:3 7 13412.8000  1:7 1:15 1:3 6 135 12.8000  1:7 1:31 1:1 6 136 12.9620  1:01:63  1:15 10 137 13.1282  1:1 1:15  1:31 9 138 13.1282  1:1 1:63 1:7 9139 13.4737  1:3 1:15  1:15 8 140 13.4737  1:3 1:63 1:3 8 141 14.2222 1:7 1:15 1:7 7 142 14.2222  1:7 1:63 1:1 7 143 14.6286  1:3 1:15  1:31 9144 15.0588  1:7 1:15  1:15 8 145 15.5152  1:7 1:15  1:31 9 146 16.0000  1:15 N/A N/A 5 147 16.2540  1:0 1:31  1:31 10 148 16.2540   1:15 1:3131:1  10 149 16.3840   1:15 1:63 31:1  11 150 16.5161  1:1 1:31  1:15 9151 16.5161   1:15 1:31 15:1  9 152 16.7869   1:15 1:63 15:1  10 15317.0667  1:3 1:31 1:7 8 154 17.0667   1:15 1:31 7:1 8 155 17:6552   1:151:63 7:1 9 156 18.2857  1:7 1:31 1:3 7 157 18.2857   1:15 1:31 3:1 7 15819.6923   1:15 1:63 3:1 8 159 21.3333   1:15 1:31 1:1 6 160 21.5579  1:01:63  1:31 11 161 21.7872  1:1 1:31  1:31 10 162 21.7872  1:1 1:63  1:1510 163 22.2609  1:3 1:31  1:15 9 164 22.2609  1:3 1:63 1:7 9 16523.2727  1:7 1:31 1:7 8 166 23.2727  1:7 1:63 1:3 8 167 25.6000   1:151:31 1:3 7 168 25.6000   1:15 1:63 1:1 7 169 26.2564  1:3 1:31  1:31 10170 26.9474  1:7 1:31  1:15 9 171 28.4444   1:15 1:31 1:7 8 172 29.2571 1:7 1:31  1:31 10 173 30.1176   1:15 1:31  1:15 9 174 31.0303   1:151:31  1:31 10 175 32.0000   1:31 N/A N/A 6 176 32.5079  1:1 1:63  1:3111 177 32.5079   1:31 1:63 31:1  11 178 33.0323  1:3 1:63  1:15 10 17933.0323   1:31 1:63 15:1  10 180 34.1333  1:7 1:63 1:7 9 181 34.1333  1:31 1:63 7:1 9 182 36.5714   1:15 1:63 1:3 8 183 36.5714   1:31 1:633:1 8 184 42.6667   1:31 1:63 1:1 7 185 43.5745  1:3 1:63  1:31 11 18644.5217  1:7 1:63  1:15 10 187 46.5455   1:15 1:63 1:7 9 188 51.2000  1:31 1:63 1:3 8 190 52.5128  1:7 1:63  1:31 11 191 53.8947   1:15 1:63 1:15 10 192 56.8889   1:31 1:63 1:7 9 193 58.5143   1:15 1:63  1:31 11194 60.2353   1:31 1:63  1:15 10 195 62.0606   1:31 1:63  1:31 11 19664.0000   1:63 N/A N/A 7

Electrowetting-Based Droplet Actuation on a Single-Sided Electrode Array

[0182] The aspects of the invention thus far have been described inconnection with the use of a droplet actuating apparatus that has atwo-sided electrode configuration such as microactuator mechanism 10illustrated in FIG. 1. That is, lower plane 12 contains control or driveelectrodes E₁-E₃ and upper plane 14 contains ground electrode G. Asregards microactuator mechanism 10, the function of upper plane 14 is tobias droplet D at the ground potential or some other referencepotential. The grounding (or biasing to reference) of upper plane 14 inconnection with the selective biasing of drive electrodes E₁-E₃ of lowerplane 12 generates a potential difference that enables droplet D to bemoved by the step-wise electrowetting technique described herein.However, in accordance with another embodiment of the invention, thedesign of the apparatus employed for two-dimensionalelectrowetting-based droplet manipulation can be simplified and mademore flexible by eliminating the need for a grounded upper plane 14.

[0183] Referring now to FIGS. 23A and 23B, a single-sided electrowettingmicroactuator mechanism, generally designated 500, is illustrated.Microactuator mechanism 500 comprises a lower plane 512 similar to thatof mechanism 10 of FIG. 1, and thus includes a suitable substrate 521 onwhich two-dimensional array of closely packed drive electrodes E (e.g.,drive electrodes E₁-E₃ and others) are embedded such as by patterning aconductive layer of copper, chrome, ITO, and the like. A dielectriclayer 523 covers drive electrodes E. Dielectric layer 523 ishydrophobic, and/or is treated with a hydrophobic layer (notspecifically shown). As a primary difference from microactuatormechanism 10 of FIG. 1, a two-dimensional grid of conducting lines G ata reference potential (e.g., conducting lines G₁-G₆ and others) has beensuperimposed on the electrode array of microactuator mechanism 500 ofFIGS. 23A and 23B, with each conducting line G running through the gapsbetween adjacent drive electrodes E. The reference potential can be aground potential, a nominal potential, or some other potential that islower than the actuation potential applied to drive electrodes E. Eachconducting line G can be a wire, bar, or any other conductive structurethat has a much narrower width/length aspect ratio in relation to driveelectrodes E. Each conducting line G could alternatively comprise aclosely packed series of smaller electrodes, but in most cases thisalternative would impractical due to the increased number of electricalconnections that would be required.

[0184] Importantly, the conducting line grid is coplanar orsubstantially coplanar with the electrode array. The conducting linegrid can be embedded on lower plane 512 by means of microfabricationprocesses commonly used to create conductive interconnect structures onmicrochips. It thus can be seen that microactuator mechanism 500 can beconstructed as a single-substrate device. It is preferable, however, toinclude an upper plane 514 comprising a plate 525 having a hydrophobicsurface 527, such as a suitable plastic sheet or a hydrophobized glassplate. Unlike microactuator mechanism 10 of FIG. 1, however, upper plane514 of microactuator mechanism 500 of FIGS. 23A and 23B does notfunction as an electrode to bias droplet D. Instead, upper plane 514functions solely as a structural component to contain droplet D and anyfiller fluid such as an inert gas or immiscible liquid.

[0185] In the use of microactuator mechanism 500 forelectrowetting-based droplet manipulations, it is still a requirementthat a ground or reference connection to droplet D be maintainedessentially constantly throughout the droplet transport event. Hence,the size or volume of droplet D is selected to ensure that droplet Doverlaps all adjacent drive electrodes E as well as all conducting linesG surrounding the drive electrode on which droplet D resides (e.g.,electrode E₂ in FIG. 23B). Moreover, it is preferable that dielectriclayer 523 be patterned to cover only drive electrodes E so thatconducting lines G are exposed to droplet D or at least are notelectrically isolated from droplet D. At the same time, however, it ispreferable that conducting lines G be hydrophobic along with driveelectrodes E so as not to impair movement of droplet D. Thus, in apreferred embodiment, after dielectric layer 523 is patterned, bothdrive electrodes E and conducting lines G are coated or otherwisetreated so as render them hydrophobic. The hydrophobization ofconducting lines G is not specifically shown in FIGS. 23A and 23B. Itwill be understood, however, that the hydrophobic layer coveringconducting lines G is so thin that an electrical contact between dropletD and conducting lines G can still be maintained, due to the porosity ofthe hydrophobic layer.

[0186] To operate microactuator mechanism 500, a suitable voltage sourceV and electrical lead components are connected with conducting lines Gand drive electrodes E. Because conducting lines G are disposed in thesame plane as drive electrodes E, application of an electrical potentialbetween conducting lines G and a selected one of drive electrodes E₁,E₂, or E₃ (with the selection being represented by switches S₁-S₃ inFIG. 23A) establishes an electric field in the region of dielectriclayer 523 beneath droplet D. Analogous to the operation of microactuatormechanism 10 of FIG. 1, the electric field in turn creates a surfacetension gradient to cause droplet D overlapping the energized electrodeto move toward that electrode (e.g., drive electrode E₃ if movement isintended in right-hand direction in FIG. 23A). The electrode array canbe sequenced in a predetermined manner according to a set of softwareinstructions, or in real time in response to a suitable feedbackcircuit.

[0187] It will thus be noted that microactuator mechanism 500 with itssingle-sided electrode configuration can be used to implement allfunctions and methods described hereinabove in connection with thetwo-sided electrode configuration of FIG. 1, e.g., dispensing,transporting, merging, mixing, incubating, splitting, analyzing,monitoring, reacting, detecting, disposing, and so on to realize aminiaturized lab-on-a-chip system. For instance, to move droplet D shownin FIG. 23B to the right, drive electrodes E₂ and E₃ are activated tocause droplet D to spread onto drive electrode E₃. Subsequentde-activation of drive electrode E₂ causes droplet D to relax to a morefavorable lower energy state, and droplet D becomes centered on driveelectrode E₃. As another example, to split droplet D, drive electrodesE₁, E₂ and E₃ are activated to cause droplet D to spread onto driveelectrodes E₁ and E₃. Drive electrode E₂ is then de-activated to causedroplet D to break into two droplets respectively centered on driveelectrodes E₁ and E₃.

[0188] Referring now to FIGS. 24A-24D, an alternative single-sidedelectrode configuration is illustrated in accordance with the presentinvention. A base substrate containing an array of row and columnbiasing electrodes E_(ij) is again utilized as in previously describedembodiments. Referring specifically to FIG. 24A, an array or portion ofan array is shown in which three rows of electrodes E₁₁-E₁₄, E₂₁-E₂₅,and E₃₁-E₃₄, respectively, are provided. The rows and columns of theelectrode array can be aligned as described herein for other embodimentsof the invention. Alternatively, as specifically shown in FIG. 24A, thearray can be misaligned such that the electrodes in any given row areoffset from the electrodes of adjacent rows. For instance, electrodesE₁₁-E₁₄ of the first row and electrodes E₃₁-E₃₄ of the third row areoffset from electrodes E₂₁-E₂₅ of the intermediate second row. Whetheraligned or misaligned, the electrode array is preferably covered withinsulating and hydrophobic layers as in previously describedembodiments. As in the configuration illustrated in FIGS. 23A and 23B, atop plate (not shown) can be provided for containment but does notfunction as an electrode.

[0189] In operation, selected biasing electrodes E_(ij) are dynamicallyassigned as either driving electrodes or grounding (or reference)electrodes. To effect droplet actuation, the assignment of a givenelectrode as a drive electrode requires that an adjacent electrode beassigned as a ground or reference electrode to create a circuitinclusive with droplet D and thereby enable the application of anactuation voltage. In FIG. 24A, electrode E₂₁ is energized and thusserves as the drive electrode, and electrode E₂₂ is grounded orotherwise set to a reference potential. All other electrodes E_(ij) ofthe illustrated array, or at least those electrodes surrounding thedriving/reference electrode pair E₂₁/E₂₂, remain in an electricallyfloating state. As shown in FIG. 24A, this activation causes droplet Doverlapping both electrodes E₂₁ and E₂₂ to seek an energeticallyfavorable state by moving so as to become centered along the gap orinterfacial region between electrodes E₂₁ and E₂₂.

[0190] In FIG. 24B, electrode E₂₁ is deactivated and electrode E₁₁ froman adjacent row is activated to serve as the next driving electrode.Electrode E₂₂ remains grounded or referenced. This causes droplet D tocenter itself between electrodes E₂, and E₂₂ by moving in a resultantnortheast direction, as indicated by the arrow. As shown in FIG. 24C,droplet D is actuated to the right along the gap between the first twoelectrode rows by deactivating electrode E₁₁ and activating electrodeE₁₂. As shown in FIG. 24D, electrode E₂₂ is disconnected from ground orreference and electrode E₂₃ is then grounded or referenced to causedroplet D to continue to advance to the right. It can be seen thatadditional sequencing of electrodes E_(ij) to render them either drivingor reference electrodes can be performed to cause droplet D to move inany direction along any desired flow path on the electrode array. It canbe further seen that, unlike previously described embodiments, the flowpath of droplet transport occurs along the gaps between electrodesE_(ij) as opposed to along the centers of electrodes E_(ij) themselves.It is also observed that the required actuation voltage will in mostcases be higher as compared with the configuration shown in FIGS. 23Aand 23B, because the dielectric layer covers both the driving andreference electrodes and thus its thickness is effectively doubled.

[0191] Referring now to FIGS. 25A and 25B, an electrode array withaligned rows and columns can be used to cause droplet transport instraight lines in either the north/south (FIG. 25A) or east/west (FIG.25B) directions. The operation is analogous to that just described withreference to FIGS. 24A-24D. That is, programmable sequencing of pairs ofdrive and reference electrodes causes the movement of droplet D alongthe intended direction. In FIG. 25A, electrodes E₁₂, E₂₂ and E₃₂ of onecolumn are selectively set to a ground or reference potential andelectrodes E₁₃, E₂₃ and E₃₃ of an adjacent column are selectivelyenergized. In FIG. 25B, electrodes E₁₁, E₁₂, E₁₃ and E₁₄ of one row areselectively energized and electrodes E₂₁, E₂₂, E₂₃ and E₂₄ of anadjacent row are selectively grounded or otherwise referenced.

[0192] It will be noted that a microactuator mechanism provided with thealternative single-sided electrode configurations illustrated in FIGS.24A-24D and FIGS. 25A and 25B can be used to implement all functions andmethods described hereinabove in connection with the two-sided electrodeconfiguration of FIG. 1. For instance, to split droplet D in either ofthe alternative configurations, three or more adjacent electrodes areactivated to spread droplet D and an appropriately selected interveningelectrode is then de-activated to break droplet D into two droplets.

[0193] It will be understood that various details of the invention maybe changed without departing from the scope of the invention.Furthermore, the foregoing description is for the purpose ofillustration only, and not for the purpose of limitation-the inventionbeing defined by the claims.

What is claimed is:
 1. An apparatus for manipulating droplets,comprising: (a) a substrate comprising a substrate surface; (b) an arrayof electrodes disposed on the substrate surface; (c) an array ofreference elements settable to a reference potential disposed insubstantially co-planar relation to the electrode array, each referenceelement adjacent to at least one of the electrodes; (d) a dielectriclayer disposed on the substrate surface and patterned to cover theelectrodes; and (e) an electrode selector for sequentially activatingand de-activating one or more selected electrodes of the array tosequentially bias the selected electrodes to an actuation voltage,whereby a droplet disposed on the substrate surface moves along adesired path defined by the selected electrodes.
 2. The apparatusaccording to claim 1 comprising a plate spaced from the substratesurface by a distance to define a space between the plate and thesubstrate surface, wherein the distance is sufficient to contain adroplet disposed in the space.
 3. The apparatus according to claim 2wherein the plate comprises a plate surface facing the substratesurface, and the plate surface is hydrophobic.
 4. The apparatusaccording to claim 2 comprising a filler fluid disposed in the space. 5.The apparatus according to claim 1 wherein at least outer portions ofthe electrodes and the reference elements are respectivelyhydrophobized.
 6. The apparatus according to claim 1 comprising ahydrophobic film disposed on the electrodes and the reference elements.7. The apparatus according to claim 1 wherein the array of referenceelements comprises a grid of elongate structures.
 8. The apparatusaccording to claim 1 wherein the reference elements are set to areference voltage less than the actuation voltage.
 9. The apparatusaccording to claim 1 wherein the reference elements are set to groundpotential.
 10. The apparatus according to claim 1 wherein at least aportion of the dielectric layer is hydrophobic.
 11. The apparatusaccording to claim 1 wherein the electrode selector comprises anelectronic processor.
 12. The apparatus according to claim 1 comprisinga droplet inlet communicating with the surface.
 13. The apparatusaccording to claim 12 comprising a droplet outlet communicating with thesurface.
 14. A method for actuating a droplet comprising the steps of:(a) providing the droplet on a surface comprising an array of electrodesand a substantially co-planar array of reference elements, wherein thedroplet is disposed on a first one of the electrodes, and the droplet atleast partially overlaps a second one of the electrodes and anintervening one of the reference elements disposed between the first andsecond electrodes; (b) activating the first and second electrodes tospread a least a portion of the droplet across the second electrode; and(c) de-activating the first electrode to move the droplet from the firstelectrode to the second electrode.
 15. The method according to claim 14wherein the second electrode is adjacent to the first electrode along afirst direction, the array comprises one or more additional electrodesadjacent to the first electrode along one or more additional directions,the droplet at least partially overlaps the one or more additionalelectrodes, and the method comprises the steps of: (a) selecting thefirst direction as a desired direction along which the droplet is tomove; and (b) selecting the second electrode for activation based on theselection of the first direction.
 16. The method according to claim 14wherein the activating step comprises selectively biasing the first andsecond electrodes to a drive voltage, and the de-activating stepcomprises de-coupling the first electrode from the drive voltage.
 17. Amethod for splitting a droplet into two or more droplets, comprising thesteps of: (a) providing a starting droplet on a surface comprising anarray of electrodes and a substantially co-planar array of referenceelements, wherein the electrode array comprises at least threeelectrodes comprising a first outer electrode, a medial electrodeadjacent to the first outer electrode, and a second outer electrodeadjacent to medial electrode, and the starting droplet is initiallydisposed on at least one of the three electrodes and at least partiallyoverlaps at least one other of the three electrodes; (b) activating eachof the three electrodes to spread the starting droplet across the threeelectrodes; and (c) de-activating the medial electrode to split thestarting droplet into first and second split droplets, whereby the firstsplit droplet is disposed on the first outer electrode and the secondsplit droplet is disposed on the second outer electrode.
 18. The methodaccording to claim 17 wherein the activating step comprises selectivelybiasing the three electrodes to a drive voltage, and the de-activatingstep comprises de-coupling the medial electrode from the drive voltage.19. The method according to claim 17 comprising the step of using anelectrode selector to control the activating and de-activating steps.20. The method according to claim 19 wherein the electrode selectorcomprises an electronic processor.
 21. A method for merging two or moredroplets into one droplet, comprising the steps of: (a) providing firstand second droplets on a surface comprising an array of electrodes and asubstantially co-planar array of reference elements, wherein theelectrode array comprises at least three electrodes comprising a firstouter electrode, a medial electrode adjacent to the first outerelectrode, and a second outer electrode adjacent to the medialelectrode, the first droplet is disposed on the first outer electrodeand at least partially overlaps the medial electrode, and the seconddroplet is disposed on the second outer electrode and at least partiallyoverlaps the medial electrode; (b) selecting one of the three electrodesas a destination electrode; (c) selecting two or more of the threeelectrodes for sequential activation and de-activation based on theselection of the destination electrode; and (d) sequentially activatingand de-activating the electrodes selected for sequencing to move one ofthe first and second droplets toward the other droplet or both of thefirst and second droplets toward each other, whereby the first andsecond droplets merge together to form a combined droplet on thedestination electrode.
 22. The method according to claim 21 wherein thefirst outer electrode is selected as the destination electrode, and thesequencing step comprises activating the second outer electrode and themedial electrode to spread the second droplet across the medialelectrode, de-activating the second outer electrode to move the seconddroplet away from the second outer electrode, activating the first outerelectrode to spread the first and second droplets into each other, andde-activating the medial electrode to form the combined droplet on thefirst outer electrode.
 23. The method according to claim 21 wherein thesecond outer electrode is selected as the destination electrode, and thesequencing step comprises activating the first outer electrode and themedial electrode to spread the first droplet across the medialelectrode, de-activating the first outer electrode to move the firstdroplet away from the first outer electrode, activating the second outerelectrode to spread the first and second droplets into each other, andde-activating the medial electrode to form the combined droplet on thesecond outer electrode.
 24. The method according to claim 21 wherein themedial electrode is selected as the destination electrode, and thesequencing step comprises activating the first outer electrode, themedial electrode, and the second outer electrode to spread the first andsecond droplets across the medial electrode and into each other, andde-activating the first and second outer electrodes to move the firstand second droplets away from the first and second outer electrodes,respectively, and form the combined droplet on the medial electrode. 25.The method according to claim 21 comprising the step of sequentiallyactivating and de-activating other electrodes of the electrode array tomove the first droplet into electrical communication with the firstouter electrode prior to forming the combined droplet.
 26. The methodaccording to claim 21 wherein the step of sequentially activating andde-activating the electrodes selected for sequencing comprisessequentially biasing one or more of the selected electrodes to a drivevoltage and de-coupling one of more of the selected electrodes from thedrive voltage.
 27. The method according to claim 21 wherein the firstdroplet comprises a first composition, the second droplet comprises asecond composition, and the combined droplet comprises the first andsecond compositions, the method further comprising the step of mixingthe first and second compositions together.
 28. The method according toclaim 27 wherein the step of forming the combined droplet mixes thefirst and second compositions together.
 29. The method according toclaim 27 wherein the mixing step comprises passively mixing the firstand second compositions together by allowing diffusion to occur withinthe combined droplet.
 30. The method according to claim 27 wherein themixing step comprises moving the combined droplet on a two-by-twosub-array of four electrodes by sequentially activating andde-activating the four electrodes to rotate the combined droplet. 31.The method according to claim 30 wherein at least a portion of thecombined droplet remains substantially stationary at or near anintersecting region of the four electrodes while the combined dropletrotates.
 32. The method according to claim 27 wherein the mixing stepcomprises sequentially activating and de-activating a linearly arrangedset of electrodes of the electrode array to oscillate the combineddroplet back and forth along the linearly arranged electrode set adesired number of times and at a desired frequency.
 33. The methodaccording to claim 27 wherein the mixing step comprises selecting a setof electrodes of the electrode array as mixing electrodes, andsequentially activating and de-activating one or more of the mixingelectrodes to split the combined droplet into two or more split dropletsand oscillate the split droplets along one or more linear paths adesired number of times and at a desired frequency.
 34. The methodaccording to claim 33 comprising the step of merging the splitelectrodes to form a new combined droplet.
 35. The method according toclaim 34 comprising the steps of splitting the new combined droplet intotwo or more new split droplets and oscillating the new split droplets.36. The method according to claim 27 wherein the mixing step comprisesselecting a set of electrodes of the electrode array as transportelectrodes, and sequentially activating and de-activating one or more ofthe transport electrodes to actuate the combined droplet along atransport path defined by the transport electrodes, whereby the firstand second compositions of the combined droplet become mixed together asthe combined droplet moves along the transport path.
 37. The methodaccording to claim 36 wherein the transport path comprises a repeatableloop on the electrode array, and the combined droplet is actuated alongthe loop a desired number of times.
 38. The method according to claim 27wherein the mixing step comprises selecting a set of electrodes of theelectrode array as mixing electrodes, and sequentially activating andde-activating one or more of the mixing electrodes to split the combineddroplet into two or more split droplets and move the split dropletsalong two or more paths.
 39. An apparatus for manipulating droplets,comprising: (a) a substrate comprising a substrate surface; (b) an arrayof electrodes disposed on the substrate surface; (c) a dielectric layerdisposed on the substrate surface and covering the electrodes; and (d)an electrode selector for dynamically creating a sequence of electrodepairs, each electrode pair comprising a selected first one of theelectrodes biased to a first voltage and a selected second one of theelectrodes disposed adjacent to the selected first electrode and biasedto a second voltage less than the first voltage, whereby a dropletdisposed on the substrate surface moves along a desired path runningbetween the electrode pairs created by the electrode selector.
 40. Theapparatus according to claim 39 comprising a plate spaced from thesubstrate surface by a distance to define a space between the plate andthe substrate surface, wherein the distance is sufficient to contain adroplet disposed in the space.
 41. The apparatus according to claim 39wherein the plate comprises a plate surface facing the substratesurface, and the plate surface is hydrophobic.
 42. The apparatusaccording to claim 39 comprising a filler fluid disposed in the space.43. The apparatus according to claim 39 wherein the array comprises aplurality of linearly arranged groups of electrodes and each group isoffset in relation to adjacent groups.
 44. The apparatus according toclaim 39 wherein at least outer portions of the electrodes arehydrophobized.
 45. The apparatus according to claim 39 comprising ahydrophobic film disposed on the electrodes.
 46. The apparatus accordingto claim 39 wherein at least a portion of the dielectric layer ishydrophobic.
 47. The apparatus according to claim 39 wherein theelectrode selector comprises an electronic processor.
 48. The apparatusaccording to claim 39 wherein the second voltage is a reference voltage.49. The apparatus according to claim 39 wherein the second voltage is aground state.
 50. A method for actuating a droplet comprising the stepsof: (a) providing the droplet on a surface comprising an array ofelectrodes, wherein the droplet is initially disposed on a first one ofthe electrodes and at least partially overlaps a second one of theelectrodes separated from the first electrode by a first gap; (b)biasing the first electrode to a first voltage and the second electrodeto a second voltage lower than the first voltage, whereby the dropletbecomes centered on the first gap; (c) biasing a third one of theelectrodes proximate to the first and second electrodes to a thirdvoltage higher than the second voltage to spread the droplet onto thethird electrode; and (d) removing the bias on the first electrode tomove the droplet away from the first electrode, whereby the dropletbecomes centered on a second gap between the second and thirdelectrodes.
 51. The method according to claim 50 wherein the secondvoltage is a ground state.
 52. The method according to claim 50 whereinthe first and third voltages are substantially equal.
 53. A method forsplitting a droplet into two or more droplets, comprising the steps of:(a) providing a starting droplet on a surface comprising an array ofelectrodes, wherein the electrode array comprises at least threeelectrodes comprising a first outer electrode, a medial electrodeadjacent to the first outer electrode, and a second outer electrodeadjacent to medial electrode, and the starting droplet is initiallydisposed on at least one of the three electrodes and at least partiallyoverlaps at least one other of the three electrodes; (b) biasing each ofthe three electrodes to a first voltage to spread the initial dropletacross the three electrodes; and (c) biasing the medial electrode to asecond voltage lower than the first voltage to split the initial dropletinto first and second split droplets, whereby the first split droplet isformed on the first outer electrode and the second split droplet isformed on the second outer electrode.
 54. The method according to claim53 wherein the step of biasing the three electrodes to the first voltagecomprises selectively coupling the three electrodes with a voltagesource.
 55. The method according to claim 53 wherein the second voltageis approximately zero.
 56. A method for merging two or more dropletsinto one droplet, comprising the steps of: (a) providing first andsecond droplets on a surface comprising an array of electrodes, whereinthe electrode array comprises at least three electrodes comprising afirst outer electrode, a medial electrode adjacent to the first outerelectrode, and a second outer electrode adjacent to the medialelectrode, the first droplet is disposed on the first outer electrodeand at least partially overlaps the medial electrode, and the seconddroplet is disposed on the second outer electrode and at least partiallyoverlaps the medial electrode; (b) selecting one of the three electrodesas a destination electrode; (c) selecting two or more of the threeelectrodes for sequential biasing based on the selection of thedestination electrode; and (d) sequentially biasing the electrodesselected for sequencing between a first voltage and a second voltage tomove one of the first and second droplets toward the other droplet orboth of the first and second droplets toward each other, whereby thefirst and second droplets merge together to form a combined droplet onthe destination electrode.
 57. The method according to claim 56 whereinthe first outer electrode is selected as the destination electrode, andthe sequential biasing step comprises biasing the second outer electrodeand the medial electrode to the first voltage to spread the seconddroplet across the medial electrode, biasing the second outer electrodeto the second voltage to move the second droplet away from the secondouter electrode, biasing the first outer electrode to the first voltageto spread the first and second droplets into each other, and biasing themedial electrode to the second voltage to form the combined droplet onthe first outer electrode.
 58. The method according to claim 56 whereinthe second outer electrode is selected as the destination electrode, andthe sequential biasing step comprises biasing the first outer electrodeand the medial electrode to the first voltage to spread the firstdroplet across the medial electrode, biasing the first outer electrodeto the second voltage to move the first droplet away from the firstouter electrode, biasing the second outer electrode to the first voltageto spread the first and second droplets into each other, and biasing themedial electrode to the second voltage to form the combined droplet onthe second outer electrode.
 59. The method according to claim 56 whereinthe medial electrode is selected as the destination electrode, and thesequential biasing step comprises biasing the first outer electrode, themedial electrode, and the second outer electrode to the first voltage tospread the first and second droplets across the medial electrode andinto each other, and biasing the first and second outer electrodes tothe second voltage to move the first and second droplets away from thefirst and second outer electrodes, respectively, and form the combineddroplet on the medial electrode.
 60. The method according to claim 56comprising the step of sequentially biasing other electrodes of theelectrode array to move the first droplet into electrical communicationwith the first outer electrode prior to forming the combined droplet.61. The method according to claim 56 wherein the second voltage isapproximately zero.
 62. The method according to claim 56 wherein thefirst droplet comprises a first composition, the second dropletcomprises a second composition, and the combined droplet comprises thefirst and second compositions, the method further comprising the step ofmixing the first and second compositions together.
 63. The methodaccording to claim 62 wherein the step of forming the combined dropletmixes the first and second compositions together.
 64. The methodaccording to claim 62 wherein the mixing step comprises passively mixingthe first and second compositions together by allowing diffusion tooccur within the combined droplet.
 65. The method according to claim 62wherein the mixing step comprises moving the combined droplet on atwo-by-two sub-array of four electrodes by sequentially biasing each ofthe four electrodes to rotate the combined droplet.
 66. The methodaccording to claim 65 wherein at least a portion of the combined dropletremains substantially stationary at or near an intersecting region ofthe four electrodes while the combined droplet rotates.
 67. The methodaccording to claim 62 wherein the mixing step comprises sequentiallyactivating and de-activating a linearly arranged set of electrodes ofthe electrode array to oscillate the combined droplet back and forthalong the linearly arranged electrode set a desired number of times andat a desired frequency.
 68. The method according to claim 62 wherein themixing step comprises selecting a set of electrodes of the electrodearray as mixing electrodes, and sequentially biasing one or more of themixing electrodes to split the combined droplet into two or more splitdroplets and oscillate the split droplets along one or more linear pathsa desired number of times and at a desired frequency.
 69. The methodaccording to claim 68 comprising the step of merging the splitelectrodes to form a new combined droplet.
 70. The method according toclaim 69 comprising the steps of splitting the new combined droplet intotwo or more new split droplets and oscillating the new split droplets.71. The method according to claim 62 wherein the mixing step comprisesselecting a set of electrodes of the electrode array as transportelectrodes, and sequentially biasing one or more of the transportelectrodes to actuate the combined droplet along a transport pathdefined by the transport electrodes, whereby the first and secondcompositions of the combined droplet become mixed together as thecombined droplet moves along the transport path.
 72. The methodaccording to claim 71 wherein the transport path comprises a repeatableloop on the electrode array, and the combined droplet is actuated alongthe loop a desired number of times.
 73. The method according to claim 62wherein the mixing step comprises selecting a set of electrodes of theelectrode array as mixing electrodes, and sequentially biasing one ormore of the mixing electrodes to split the combined droplet into two ormore split droplets and move the split droplets along two or more paths.74. A method for sampling a continuous liquid flow, comprising the stepsof: (a) supplying a liquid flow to a surface along a first flow path,the surface comprising an array of electrodes and a substantiallyco-planar array of reference elements, wherein at least a portion of theliquid flow is disposed on a first one of the electrodes and at leastpartially overlaps a second one of the electrodes and a referenceelement between the first and second electrodes; (b) activating thefirst electrode, the second electrode, and a third one of the electrodesadjacent to the second electrode to spread the liquid flow portionacross the second and third electrodes; (c) de-activating the secondelectrode to form a droplet from the liquid flow on the third electrode,whereby the droplet is distinct from and controllable independently ofthe liquid flow.
 75. The method according to claim 74 comprising thestep of moving the droplet on the surface along a second flow path. 76.The method according to claim 75 wherein the step of moving the dropletcomprises sequentially activating and de-activating a set of electrodesof the electrode array.
 77. The method according to claim 75 comprisingthe step of activating a set of electrodes of the electrode array tocreate a processing area, and the droplet is moved along the second flowpath to the processing area.
 78. The method according to claim 74wherein the first flow path flows along the surface along an inputdirection, and the second and third electrodes are disposed along theinput direction.
 79. The method according to claim 74 wherein the firstflow path flows along the surface along an input direction, and thesecond and third electrodes are disposed along a transport directiondifferent from the input direction.
 80. The method according to claim 74comprising the step of combining the droplet with one or more additionaldroplets on the surface to form a liquid output flow stream.
 81. Amethod for sampling a continuous liquid flow, comprising the steps of:(a) supplying a liquid flow to a surface along a first flow path, thesurface comprising an array of electrodes, wherein at least a portion ofthe liquid flow is disposed on a first one of the electrodes and atleast partially overlaps a second one of the electrodes; (b) biasing thefirst electrode, the second electrode, and a third one of the electrodesadjacent to the second electrode to a first voltage to spread the liquidflow portion across the second and third electrodes; and (c) biasing thesecond electrode to a second voltage less than the first voltage to forma droplet from the liquid flow on the third electrode, whereby thedroplet is distinct from and controllable independently of the liquidflow.
 82. A binary mixing apparatus comprising: (a) first mixing unitcomprising a first surface area, an array of first electrodes disposedon the first surface area, and an array of first reference elementsdisposed in substantially co-planar relation to the first electrodes;(b) a second mixing unit comprising a second surface area, an array ofsecond electrodes disposed on the second surface area, an array ofsecond reference elements disposed in substantially co-planar relationto the second electrodes, and a droplet outlet area communicating withthe second surface area and with the first mixing unit; and (c) anelectrode selector for sequentially activating and de-activating one ormore selected first electrodes to mix together two droplets supplied tothe first surface area, and for sequentially activating andde-activating one or more selected second electrodes to mix together twoother droplets supplied to the second surface area.
 83. The apparatusaccording to claim 82 comprising a buffer unit communicating with thefirst mixing unit and the droplet outlet area and controlled by theelectrode selector.
 84. A binary mixing apparatus comprising: (a) firstmixing unit comprising a first surface area and an array of firstelectrodes disposed on the first surface area; (b) a second mixing unitcomprising a second surface area, an array of second electrodes disposedon the second surface area, and a droplet outlet area communicating withthe second surface area and with the first mixing unit; and (c) anelectrode selector for dynamically creating a sequence of firstelectrode pairs on the first surface area and a sequence of secondelectrode pairs on the second surface area, each first electrode paircomprising a selected first electrode biased to a first voltage and aselected first electrode biased to a second voltage less than the firstvoltage, each second electrode pair comprising a selected secondelectrode biased to a third voltage and a selected second electrodebiased to a fourth voltage less than the third voltage, whereby twodroplets supplied to the first surface area are actuated by the firstelectrode pairs to mix together and two other droplets supplied to thesecond surface area are actuated by the second electrode pairs to mixtogether.
 85. A method for producing a droplet having a desired mixingratio, comprising the steps of: (a) providing a surface, an array ofelectrodes disposed on the surface, and an array of conducting elementsdisposed in substantially co-planar relation to the electrode array; (b)providing a sample droplet having an initial concentration and a diluentdroplet on the surface; (c) merging the sample droplet with the diluentdroplet to form a combined droplet by sequentially energizing andde-energizing a selected set of the electrodes; and (d) mixing thecombined droplet to reduce its concentration below the initialconcentration of the sample droplet, whereby the reduced concentrationof the combined droplet corresponds to an approximate mixing ratio. 86.The method according to claim 85 comprising the step of repeating themerging and mixing steps for a determined number of times using one ormore additional diluent droplets to form one or more new combineddroplets until the reduced concentration of the last combined dropletapproaches the desired mixing ratio within a desired range of accuracy.87. The method according to claim 85 comprising the steps of splittingthe mixed combined droplet into two mixed droplets, merging at least oneof the two mixed droplets with an additional diluent droplet to form anew combined droplet, and mixing the new combined droplet.
 88. Themethod according to claim 85 comprising the step of, after mixing thecombined droplet, determining whether the approximate mixing ratio ofthe combined droplet approaches the desired mixing ratio within thedesired range of accuracy.
 89. The method according to claim 88 whereinthe step of determining comprises measuring a value representative ofthe reduced concentration of the combined droplet and comparing themeasured value to a determined set point value representative of thedesired mixing ratio.
 90. The method according to claim 88 wherein, ifit is determined that the approximate mixing ratio of the combineddroplet has not approached the desired mixing ratio within a desiredrange of accuracy, merging the combined droplet with a new diluentdroplet to form a new combined droplet having a concentration moreclosely approaching the desired mixing ratio.
 91. A method for producinga droplet having a desired mixing ratio, comprising the steps of: (a)providing an array of electrodes disposed on a surface; (b) providing asample droplet having an initial concentration and a diluent droplet onthe surface; (c) merging the sample droplet with the diluent droplet toform a combined droplet by dynamically creating a sequence of electrodepairs from the array, each electrode pair comprising a selected firstone of the electrodes biased to a first voltage and a selected secondone of the electrodes biased to a second voltage less than the firstvoltage, whereby one of or both the sample droplet and the diluentdroplet are actuated along a path defined by the sequence of electrodepairs; and (d) mixing the combined droplet to reduce its concentrationbelow the initial concentration of the sample droplet, whereby thereduced concentration of the combined droplet corresponds to anapproximate mixing ratio.
 92. The method according to claim 91 whereinthe mixing step comprises dynamically creating an additional sequence ofelectrode pairs from the array to actuate the combined droplet.
 93. Amethod for producing a droplet having a desired final mixing ratio,comprising the steps of: (a) in a first mixing unit comprising a firstsurface area, an array of first electrodes disposed on the first surfacearea, and an array of first conducting elements disposed insubstantially co-planar relation to the first electrodes, mixing a firstsample droplet with a first diluent droplet to form a first combineddroplet having a desired first intermediate mixing ratio; (b) in asecond mixing unit comprising a second surface area, an array of secondelectrodes disposed on the second surface area, and an array of secondconducting elements disposed in substantially co-planar relation to thesecond electrodes, mixing a second sample droplet with a second diluentdroplet to form a second combined droplet having a desired secondintermediate mixing ratio; (c) transporting the second combined dropletto the first mixing unit; and (d) in the first mixing unit, combiningthe first combined droplet with the second combined droplet to form athird combined droplet having the desired final mixing ratio.
 94. Amethod for producing a droplet having a desired final mixing ratio,comprising the steps of: (a) in a first mixing unit comprising an arrayof first electrodes disposed on a first surface area, mixing a firstsample droplet with a first diluent droplet by dynamically creating afirst sequence of first pairs of first electrodes, each first paircomprising a first drive electrode biased to a first voltage and a firstreference electrode biased to a second voltage less than the firstvoltage, whereby the first sample droplet and the first diluent dropletare actuated to form a first combined droplet having a desired firstintermediate mixing ratio; (b) in a second mixing unit comprising anarray of second electrodes disposed on a second surface area, mixing asecond sample droplet with a second diluent droplet by dynamicallycreating a second sequence of second pairs of second electrodes, eachsecond pair comprising a second drive electrode biased to a thirdvoltage and a second reference electrode biased to a fourth voltage lessthan the third voltage, whereby the second sample droplet and the seconddiluent droplet are actuated to form a second combined droplet having adesired second intermediate mixing ratio; (c) transporting the secondcombined droplet to the first mixing unit; and (d) in the first mixingunit, combining the first combined droplet with the second combineddroplet to form a third combined droplet having the desired final mixingratio.